Search results for: fixed point theorems

Authors: Walied Hazim Sharif

Abstract:

The problem of faithful extension with the condition of keeping constant height h and constant width w, i.e. for h w -inextensibility, seems more interesting than the brute extension of finite poset (partially ordered set). We shall investigate some theorems of hw-inextensive and hw-exrensive posets that can be used to formulate the faithful extension problem. A theorem in its general form of hw-inextensive posets is given to implement the presented theorems.

Keywords: faithful extension, poset, extension, inextension, height, width, hw-extensive, hw-inextensive

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Authors: S. Padmapriya, V. Lakshmi Prabha

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In this paper, an efficient reconfigurable fixed-point Least Mean Square Adaptive FIR filter is proposed. The proposed architecture has two methods of operation: one is area efficient design and the other is optimized power. Pipelining of the adder blocks and partial product generator are used to achieve low area and reversible logic is used to obtain low power design. Depending upon the input samples and filter coefficients, one of the techniques is chosen. Least-Mean-Square adaptation is performed to update the weights. The architecture is coded using Verilog and synthesized in cadence encounter 0.18μm technology. The synthesized results show that the area reduction ratio of the proposed when compared with conventional technique is about 1.2%.

Keywords: adaptive filter, carry select adder, least mean square algorithm, reversible logic

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Authors: Y. Heyrani Birak, R. Hizaji, J. Shahkarami

Abstract:

Reinforced Concrete (RC) deep beams are special structural elements because of their geometry and behavior under loads. For example, assumption of strain- stress distribution is not linear in the cross section. These types of beams may have simple supports or fixed supports. A lot of research works have been conducted on simply supported deep beams, but little study has been done in the fixed-end RC deep beams behavior. Recently, using of fixed-ended deep beams has been widely increased in structures. In this study, the behavior of fixed-ended deep beams is investigated, and the important parameters in capacity of this type of beams are mentioned.

Keywords: deep beam, capacity, reinforced concrete, fixed-ended

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Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

Abstract:

It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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Authors: Walied Hazim Sharif

Abstract:

The problem of faithful extension with the condition of keeping constant height h and constant width w, i.e. for hw-inextensibility, seems more interesting than the brute extension of finite poset (partially ordered set). We shall investigate some theorems of hw-inextensive and hw-extensive posets that can be used to formulate the faithful extension problem. A theorem in its general form of hw-inextensive posets are given to implement the presented theorems.

Keywords: faithful extension, poset, extension, inextension, height, width, hw-extensive, hw-inextensive

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves and generalizes corresponding results in the literature in two ways: the iterative process is faster, operators are more general. In the end, we indicate that the results can also be proved with the iterative process with error terms.

Keywords: contractive-like operator, iterative process, fixed point, strong convergence

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Authors: Kamel Al-Khaled

Abstract:

A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Safeer Hussain Khan, H. Fukhar-ud-Din

Abstract:

The concept of quasi-contractive type operators was given by Berinde and extended by Imoru and Olatinwo. They named this new type as contractive-like operators. On the other hand, Xu and Noo introduced a three-step-one-mappings iterative process which can be seen as a generalization of Mann and Ishikawa iterative processes. Approximating common fixed points has its own importance as it has a direct link with minimization problem. Motivated by this, in this paper, we first extend the iterative process of Xu and Noor to the case of three-step-three-mappings and then prove a strong convergence result using contractive-like operators for this iterative process. In general, this generalizes corresponding results using Mann, Ishikawa and Xu-Noor iterative processes with quasi-contractive type operators. It is to be pointed out that our results can also be proved with iterative process involving error terms.

Keywords: contractive-like operator, iterative process, common fixed point, strong convergence

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Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong

Abstract:

This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.

Keywords: asymptotically quasi-nonexpansive nonself-mapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space

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Authors: Xiaolai Zhang, Haitao Zhang, Qiwen Sun, Weixin Qian, Weiyong Ying

Abstract:

High temperature Fischer-Tropsch synthesis process use fixed fluidized bed as a reactor. In order to understand the flow behavior in the fluidized bed better, the research of how the radial velocity affect the entire flow field is necessary. Laser Doppler Velocimetry (LDV) was used to study the radial velocity distribution along the diameter direction of the cross-section of the particle in a fixed fluidized bed. The velocity in the cross-section is fluctuating within a small range. The direction of the speed is a random phenomenon. In addition to r/R is 1, the axial velocity are more than 6 times of the radial velocity, the radial velocity has little impact on the axial velocity in a fixed fluidized bed.

Keywords: Fischer-Tropsch synthesis, Fixed fluidized bed, LDV, Velocity

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Authors: Zhenjie Liu

Abstract:

This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

Keywords: mixed monotone operator, boundary value problem, time scale, green's function, positive solution, singularity

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Authors: Tulin Coskun

Abstract:

We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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Authors: R. Vigneswaran, S. Thilakanathan

Abstract:

Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Shashi Kant Mishra

Abstract:

In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

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Authors: Karim S. Hassan, Hisham M. Hamed, Yassmine A. Fahmy, Ahmed F. Shalash

Abstract:

The mismatch between in-phase and quadrature signals in Orthogonal frequency division multiplexing (OFDM) systems, such as DVB-T2, results in a severe degradation in performance. Several general solutions have been proposed in the past, but these are largely computationally intensive, leading to complex implementations. In this paper, we propose a relatively simple iterative solution, which provides good results in relatively few iterations, using fixed precision arithmetic. An additional advantage is that complex digital blocks, such as dividers and square root, are not required. Thus, the proposed solution may be implemented in relatively simple hardware.

Keywords: OFDM, DVB-T2, I/Q imbalance, I/Q mismatch, iterative method, fixed point, reduced complexity

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Authors: Tiago Sampaio, André Vasconcelos, Bruno Fragoso

Abstract:

The Normalized Systems Theory, which is designed to be applied to software architectures, provides a set of theorems, elements and rules, with the purpose of enabling evolution in Information Systems, as well as ensuring that they are ready for change. In order to make that possible, this work’s solution is to apply the Normalized Systems Theory to the domain of enterprise architectures, using Archimate. This application is achieved through the adaptation of the elements of this theory, making them artifacts of the modeling language. The theorems are applied through the identification of the viewpoints to be used in the architectures, as well as the transformation of the theory’s encapsulation rules into architectural rules. This way, it is possible to create normalized enterprise architectures, thus fulfilling the needs and requirements of the business. This solution was demonstrated using the Portuguese Public Procurement System. The Portuguese government aims to make this system as fair as possible, allowing every organization to have the same business opportunities. The aim is for every economic operator to have access to all public tenders, which are published in any of the 6 existing platforms, independently of where they are registered. In order to make this possible, we applied our solution to the construction of two different architectures, which are able of fulfilling the requirements of the Portuguese government. One of those architectures, TO-BE A, has a Message Broker that performs the communication between the platforms. The other, TO-BE B, represents the scenario in which the platforms communicate with each other directly. Apart from these 2 architectures, we also represent the AS-IS architecture that demonstrates the current behavior of the Public Procurement Systems. Our evaluation is based on a comparison between the AS-IS and the TO-BE architectures, regarding the fulfillment of the rules and theorems of the Normalized Systems Theory and some quality metrics.

Keywords: archimate, architecture, broker, enterprise, evolvable systems, interoperability, normalized architectures, normalized systems, normalized systems theory, platforms

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Authors: Adel Bouchakhchoukha, Hakim Akeb

Abstract:

In this work, we propose a hybrid heuristic in order to solve the Team Orienteering Problem (TOP). Given a set of points (or customers), each with associated score (profit or benefit), and a team that has a fixed number of members, the problem to solve is to visit a subset of points in order to maximize the total collected score. Each member performs a tour starting at the start point, visiting distinct customers and the tour terminates at the arrival point. In addition, each point is visited at most once, and the total time in each tour cannot be greater than a given value. The proposed heuristic combines beam search and a local optimization strategy. The algorithm was tested on several sets of instances and encouraging results were obtained.

Keywords: team orienteering problem, vehicle routing, beam search, local search

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Authors: Mohammad Ali Alavidoost, Hossein Bozorgian

Abstract:

Criterion-referenced tests (CRTs) are designed to measure student performance against a fixed set of predetermined criteria or learning standards. The reliability of such tests cannot be based on internal reliability. Threshold loss agreement is one way to calculate the reliability of CRTs. However, the selection of master and non-master in such agreement is determined by the threshold point. The problem is if the threshold point witnesses a minute change, the selection of master and non-master may have a drastic change, leading to the change in reliability results. Therefore, in this study, the Fuzzy logic approach is employed as a remedial procedure for data analysis to obviate the threshold point problem. Forty-one Iranian students were selected; the participants were all between 20 and 30 years old. A quantitative approach was used to address the research questions. In doing so, a quasi-experimental design was utilized since the selection of the participants was not randomized. Based on the Fuzzy logic approach, the threshold point would be more stable during the analysis, resulting in rather constant reliability results and more precise assessment.

Keywords: criterion-referenced tests, threshold loss agreement, threshold point, fuzzy logic approach

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Authors: Fayssal Amrane, Azeddine Chaiba

Abstract:

In this paper, type-2 fuzzy logic control (T2FLC) and neuro-fuzzy control (NFC) for a doubly fed induction generator (DFIG) based on direct power control (DPC) with a fixed switching frequency is proposed for wind generation application. First, a mathematical model of the doubly-fed induction generator implemented in d-q reference frame is achieved. Then, a DPC algorithm approach for controlling active and reactive power of DFIG via fixed switching frequency is incorporated using PID. The performance of T2FLC and NFC, which is based on the DPC algorithm, are investigated and compared to those obtained from the PID controller. Finally, simulation results demonstrate that the NFC is more robust, superior dynamic performance for wind power generation system applications.

Keywords: doubly fed induction generator (DFIG), direct power control (DPC), neuro-fuzzy control (NFC), maximum power point tracking (MPPT), space vector modulation (SVM), type 2 fuzzy logic control (T2FLC)

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Authors: Omar Eldenali, Ahmed M. Bufares

Abstract:

There are primarily two types of Unmanned Aerial Vehicle (UAVs), namely, multirotor and fixed wing. Each type has its own advantages. This study introduces a design of a fixed wing vertical take-off and landing (VTOL) UAV. The design is classified as ready-to-fly (RTF) fixed wing UAV. This means that the UAV is capable of not only taking off, landing, or hovering like a multirotor aircraft but also cruising like a fixed wing UAV. In this study, the conceptual design of 15 kg takeoff weight twin-tail boom configuration FW-VTOL plane is carried out, the initial sizing of the plane is conducted, and both the horizontal and vertical tail configurations are estimated. Moreover, the power required for each stage of flight is determined. Finally, the stability analysis of the plane based on this design is performed, the results shows that this design based on the suggested flight mission is stable and can be utilized.

Keywords: FW-VTOL, initial sizing, constrain analysis, stability

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Authors: M. Khouil, N. Saber, M. Mestari

Abstract:

This study aimed to propose, a different architecture of a Path Planning using the NECMOP. where several nonlinear objective functions must be optimized in a conflicting situation. The ability to detect and avoid collision is very important for mobile intelligent machines. However, many artificial vision systems are not yet able to quickly and cheaply extract the wealth information. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons linear and threshold logic, which simplified the actual implementation of all the networks proposed. This article represents a comprehensive algorithm that determine through the AMAXNET network a measure (a mini-maximum point) in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: path planning, collision detection, convex polyhedron, neural network

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Authors: A. Aarabzadeh, R. Hizaji

Abstract:

Reinforced Concrete (RC) deep beams are a special type of beams due to their geometry, boundary conditions, and behavior compared to ordinary shallow beams. For example, assumption of a linear strain-stress distribution in the cross section is not valid. Little study has been dedicated to fixed-end RC deep beams. Also, most experimental studies are carried out on simply supported deep beams. Regarding recent tendency for application of deep beams, possibility of using fixed-ended deep beams has been widely increased in structures. Therefore, it seems necessary to investigate the aforementioned structural element in more details. In addition to experimental investigation of a concrete deep beam under cyclic load, different failure mechanisms of fixed-ended deep beams under this type of loading have been evaluated in the present study. The results show that failure mechanisms of deep beams under cyclic loads are quite different from monotonic loads.

Keywords: deep beam, cyclic load, reinforced concrete, fixed-ended

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Authors: Quznetsov Gunn

Abstract:

In the study of the logical foundations of probability theory, it was found that the terms and equations of the fundamental theoretical physics represent terms and theorems of the classical probability theory, more precisely, of that part of this theory, which considers the probability of dot events in the 3 + 1 space-time. In particular, the masses, moments, energies, spins, etc. turn out of parameters of probability distributions such events. The terms and the equations of the electroweak and of the quark-gluon theories turn out the theoretical-probabilistic terms and theorems. Here the relation of a neutrino to his lepton becomes clear, the W and Z bosons masses turn out dynamic ones, the cause of the asymmetry between particles and antiparticles is the impossibility of the birth of single antiparticles. In addition, phenomena such as confinement and asymptotic freedom receive their probabilistic explanation. And here we have the logical foundations of the gravity theory with phenomena dark energy and dark matter.

Keywords: classical theory of probability, logical foundation of fundamental theoretical physics, masses, moments, energies, spins

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Authors: Shoeb Ahmed Adeel, Vivek Paul, K. Prajwal, Michael Fenelon

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Techniques have been used to tether and stabilize a multi-rotor MAV but carrying out the same process to a fixed wing MAV is a novel method which can be utilized in order to reduce damage occurring to the fixed wing MAVs while conducting flight test trials and PID tuning. A few sensors and on board controller is required to carry out this experiment in horizontal and vertical plane of the vehicle. Here we will be discussing issues such as sensitivity of the air vehicle, endurance and external load of the string acting on the vehicle.

Keywords: MAV, PID tuning, tethered flight, UAV

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Meng Wu

Abstract:

Unmanned aerial vehicle (UAV) landing technology is a common task that is required to be fulfilled by fly robots. In this paper, the crazyflie2.0 is located by ultra-wideband (UWB) localization system that contains 4 UWB anchors. Another UWB anchor is introduced and installed on a stationary platform. One cost function is designed to find the minimum distance between crazyflie2.0 and the anchor installed on the stationary platform. The coordinates of the anchor are unknown in advance, and the goal of the cost function is to define the location of the anchor, which can be considered as an optimal landing point. When the cost function reaches the minimum value, the corresponding coordinates of the UWB anchor fixed on the stationary platform can be calculated and defined as the landing point. The simulation shows the effectiveness of the method in this paper.

Keywords: UAV landing, UWB localization system, UWB anchor, cost function, stationary platform

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Authors: Mitsuyoshi Tomiya, Kentaro Kawamura, Shoichi Sakamoto

Abstract:

In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space.

Keywords: chaotic billiard, Poincaré section, scar, wave packet

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Authors: Jun Li, Wenze Wang, Zhanggui Hu, Yongwei Zhu, Dunwen Zuo

Abstract:

Non-water based fixed abrasive polishing was adopted to manufacture LBO crystal for nano precision surface quality because of its deliquescent. Ethyl alcohol was selected as the non-water based slurry solvent and ethanediamine, lactic acid, hydrogen peroxide were add in the slurry as a chemical additive, respectively. Effect of different additives with non-water based slurry on material removal rate, surface topography, microscopic appearances and surface roughness were investigated in fixed abrasive polishing of LBO crystal. The results show the best surface quality of LBO crystal with surface roughness Sa 8.2 nm and small damages was obtained by non-water based slurry with lactic acid. Non-water based fixed abrasive polishing can achieve nano precision surface quality of LBO crystal with high material removal.

Keywords: non-water based slurry, LBO crystal, fixed abrasive polishing, surface roughness

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Authors: Rupu Yang, Cong Toan Tran, Assaad Zoughaib

Abstract:

The work provides an iterative nonlinear programming method to synthesize a heat exchanger network by manipulating the trade-offs between the heat load of process heat exchangers (HEs) and utilities. We consider for the synthesis problem two cases, the first one without fixed cost for HEs, and the second one with fixed cost. For the no fixed cost problem, the nonlinear programming (NLP) model with all the potential HEs is optimized to obtain the global optimum. For the case with fixed cost, the NLP model is iterated through adding/removing HEs. The method was applied in five case studies and illustrated quite well effectiveness. Among which, the approach reaches the lowest TAC (2,904,026$/year) compared with the best record for the famous Aromatic plants problem. It also locates a slightly better design than records in literature for a 10 streams case without fixed cost with only 1/9 computational time. Moreover, compared to the traditional mixed-integer nonlinear programming approach, the iterative NLP method opens a possibility to consider constraints (such as controllability or dynamic performances) that require knowing the structure of the network to be calculated.

Keywords: heat exchanger network, synthesis, NLP, optimization

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Authors: Umar Yusuf Batsari

Abstract:

Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

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