Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3237

Search results for: common fixed point

3237 Common Fixed Point Theorems for Co-Cyclic Weak Contractions in Compact Metric

Authors: Alemayehu Geremew Negash

Abstract:

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.

Keywords: Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

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3236 Simulation Tools for Fixed Point DSP Algorithms and Architectures

Authors: K. B. Cullen, G. C. M. Silvestre, N. J. Hurley

Abstract:

This paper presents software tools that convert the C/Cµ floating point source code for a DSP algorithm into a fixedpoint simulation model that can be used to evaluate the numericalperformance of the algorithm on several different fixed pointplatforms including microprocessors, DSPs and FPGAs. The tools use a novel system for maintaining binary point informationso that the conversion from floating point to fixed point isautomated and the resulting fixed point algorithm achieves maximum possible precision. A configurable architecture is used during the simulation phase so that the algorithm can produce a bit-exact output for several different target devices.

Keywords: DSP devices, DSP algorithm, simulation model, software

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3235 Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space

Authors: Alemayehu Geremew Negash

Abstract:

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.  

Keywords: Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

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3234 A Reconfigurable Processing Element for Cholesky Decomposition and Matrix Inversion

Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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3233 Two-step Iterative Process For Common Fixed Points of Two Asymptotically Quasi-nonexpansive Mappings

Authors: Safeer Hussain Khan

Abstract:

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

Keywords: Asypmtotically quasi-nonexpansive mappings, Commonfixed point, Strong and weak convergence, Iteration process.

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3232 A Reconfigurable Processing Element Implementation for Matrix Inversion Using Cholesky Decomposition

Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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3231 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

Authors: Menglong Su, Shaoyun Shi, Qing Xu

Abstract:

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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3230 Error Propagation of the Hidden-Point Bar Method: Effect of Bar Geometry

Authors: Said M. Easa, Ahmed Shaker

Abstract:

The hidden-point bar method is useful in many surveying applications. The method involves determining the coordinates of a hidden point as a function of horizontal and vertical angles measured to three fixed points on the bar. Using these measurements, the procedure involves calculating the slant angles, the distances from the station to the fixed points, the coordinates of the fixed points, and then the coordinates of the hidden point. The propagation of the measurement errors in this complex process has not been fully investigated in the literature. This paper evaluates the effect of the bar geometry on the position accuracy of the hidden point which depends on the measurement errors of the horizontal and vertical angles. The results are used to establish some guidelines regarding the inclination angle of the bar and the location of the observed points that provide the best accuracy.

Keywords: Hidden point, accuracy, error propagation, surveying, evaluation, simulation, geometry.

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3229 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

Authors: Lv Yuhua

Abstract:

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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3228 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem

Authors: Adil AL-Rammahi

Abstract:

In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

Keywords: Fredholm integral equation, power series, Banach fixed point theorem, Linear Systems.

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3227 Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions

Authors: Yasuhito Tanaka

Abstract:

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.

Keywords: sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.

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3226 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

Authors: Ismat Beg, Asma Rashid Butt

Abstract:

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn  x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x  y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x  y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0  x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

Keywords: Fixed point, partially ordered set, metric space, set valued mapping.

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3225 Convergence of a One-step Iteration Scheme for Quasi-asymptotically Nonexpansive Mappings

Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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3224 Approximating Fixed Points by a Two-Step Iterative Algorithm

Authors: Safeer Hussain Khan

Abstract:

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

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3223 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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3222 Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra

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

Abstract:

In this paper, a different architecture of a collision detection neural network (DCNN) is developed. 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. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: Collision identification, fixed time, convex polyhedra, neural network, AMAXNET.

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3221 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation

Authors: Xiguang Li

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.

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3220 Positive Solutions of Second-order Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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3219 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.

Keywords: p-Laplacian, cone, fixed point theorem, positive solution.

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3218 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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3217 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

Abstract:

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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3216 On Tarski’s Type Theorems for L-Fuzzy Isotone and L-Fuzzy Relatively Isotone Maps on L-Complete Propelattices

Authors: František Včelař, Zuzana Pátíková

Abstract:

Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Keywords: Fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity.

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3215 Motion Planning and Control of Autonomous Robots in a Two-dimensional Plane

Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper proposes a solution to the motion planning and control problem of a point-mass robot which is required to move safely to a designated target in a priori known workspace cluttered with fixed elliptical obstacles of arbitrary position and sizes. A tailored and unique algorithm for target convergence and obstacle avoidance is proposed that will work for any number of fixed obstacles. The control laws proposed in this paper also ensures that the equilibrium point of the given system is asymptotically stable. Computer simulations with the proposed technique and applications to a planar (RP) manipulator will be presented.

Keywords: Point-mass Robot, Asymptotic stability, Motionplanning, Planar Robot Arm.

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3214 An Iterated Function System for Reich Contraction in Complete b Metric Space

Authors: R. Uthayakumar, G. Arockia Prabakar

Abstract:

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

Keywords: Fractals, Iterated Function System, Compact set, Reich Contraction, Well posedness.

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3213 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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3212 On Finite Wordlength Properties of Block-Floating-Point Arithmetic

Authors: Abhijit Mitra

Abstract:

A special case of floating point data representation is block floating point format where a block of operands are forced to have a joint exponent term. This paper deals with the finite wordlength properties of this data format. The theoretical errors associated with the error model for block floating point quantization process is investigated with the help of error distribution functions. A fast and easy approximation formula for calculating signal-to-noise ratio in quantization to block floating point format is derived. This representation is found to be a useful compromise between fixed point and floating point format due to its acceptable numerical error properties over a wide dynamic range.

Keywords: Block floating point, Roundoff error, Block exponent dis-tribution fuction, Signal factor.

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3211 Algorithms for Computing of Optimization Problems with a Common Minimum-Norm Fixed Point with Applications

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: σ-asymptotically quasi-nonexpansive nonselfmapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space.

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3210 Hydrodynamic Simulation of Fixed Bed GTL Reactor Using CFD

Authors: Sh. Shahhosseini, S. Alinia, M. Irani

Abstract:

In this work, axisymetric CFD simulation of fixed bed GTL reactor has been conducted, using computational fluid dynamics (CFD). In fixed bed CFD modeling, when N (tube-to-particle diameter ratio) has a large value, it is common to consider the packed bed as a porous media. Synthesis gas (a mixture of predominantly carbon monoxide and hydrogen) was fed to the reactor. The reactor length was 20 cm, divided to three sections. The porous zone was in the middle section of the reactor. The model equations were solved employing finite volume method. The effects of particle diameter, bed voidage, fluid velocity and bed length on pressure drop have been investigated. Simulation results showed these parameters could have remarkable impacts on the reactor pressure drop.

Keywords: GTL Process, Fixed bed reactor, Pressure drop, CFDsimulation.

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3209 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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3208 Unique Positive Solution of Nonlinear Fractional Differential Equation Boundary Value Problem

Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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