Search results for: Banach space
1421 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12351420 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14571419 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16661418 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16261417 Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems
Authors: M. H. M. Rashid
Abstract:
A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7681416 Positive Solutions of Initial Value Problem for the Systems of Second Order Integro-Differential Equations in Banach Space
Authors: Lv Yuhua
Abstract:
In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results (see[5,6]), and the results is new even in finite dimensional spaces.
Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14891415 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24771414 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10891413 Hyers-Ulam Stability of Functional Equationf(3x) = 4f(3x − 3) + f(3x − 6)
Authors: Soon-Mo Jung
Abstract:
The functional equation f(3x) = 4f(3x-3)+f(3x- 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X, where X is a real Banach space.Keywords: Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13441412 Banach Lattices with Weak Dunford-Pettis Property
Authors: Khalid Bouras, Mohammed Moussa
Abstract:
We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results.
Keywords: Almost Dunford-Pettis operator, weak Dunford-Pettis operator, eak almost Dunford-Pettis operator, almost Dunford-Pettis operator, weak Dunford-Pettis operator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20191411 Existence of Solution for Boundary Value Problems of Differential Equations with Delay
Authors: Xiguang Li
Abstract:
In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.
Keywords: Banach space, boundary value problem, differential equation, delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12201410 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition
Abstract:
This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.
Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16471409 Almost Periodicity in a Harvesting Lotka-Volterra Recurrent Neural Networks with Time-Varying Delays
Authors: Yongzhi Liao
Abstract:
By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.
Keywords: positive almost periodic solution, Lotka-Volterra, neural networks, Banach fixed point theorem, harvesting
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16081408 PIL Theory
Authors: A. Peveri
Abstract:
The curvature space-time by the presence of material, this deformation must present a pattern of deformation, not random. Space is uniform, elastic and any modification that occurs in one part, causes a change in another.
This deformation exists, must be a constant value and is independent of the observer, and relates the amount of matter, the force caused by the curvature of space and surface space. This unit of space is defined in this study as PIL and represents a constant area of space, deformable in the direction and sense of the center of mass of the body. The PIL is curved and connected to the center of mass of the Earth, to get to that point, through all matter, thus forming part of any place between particles at atomic and subatomic levels. At these levels the space between each particle is flat, unlike the macro where the space curves.
Keywords: Space flat, Space curved, Unit of space, Deformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14981407 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces
Authors: R. Uthayakumar, D. Easwaramoorthy
Abstract:
This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.Keywords: Fractal Analysis, Fixed Point, Contraction, Iterated Function System, Intuitionistic Fuzzy Metric Space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18421406 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12901405 Necessary and Sufficient Condition for the Quaternion Vector Measure
Authors: Mei Li, Fahui Zhai
Abstract:
In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.Keywords: Quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12641404 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14011403 A New Class F2 (M, 0, N)L„ p)F of The Double Difference Sequences of Fuzzy Numbers
Authors: N. Subramanian, C. Murugesan
Abstract:
The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.
Keywords: Orlicz function, solid space, metric space, completeness
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10001402 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14361401 Need of National Space Legislation for Space Faring Nations
Authors: Muhammad Naveed, Yang Caixia
Abstract:
The need for national space legislation is pivotal, particularly in light of the fact that in recent years space activities have grown immensely both in volume and diversity. Countries are progressively developing capabilities in space exploration and scientific discoveries, market their capabilities to manufacture satellites, provide launch services from their facilities and are looking to privatize and commercialize their space resources. Today, nations are also seeking to comprehend the technological and financial potential of the private sector and are considering to share their financial burdens with them and to limit their exposures to risks, but they are lagging behind in legal framework in this regard. In the perspective of these emerging developments, it is therefore, felt that national space legislation should be enacted with the goal of building and implementing a vibrant and transparent legal framework at the national level to hasten investments and to ensure growth in this capital intensive - highly yield strategic sector. This study looks at (I) the international legal framework that governs space activities; (II) motivation behind making national space laws; and (III) the need for national space legislation. The paper concludes with some recommendations with regards to the conceivable future direction for national space legislation, in particular space empowered sub-areas for countries.
Keywords: International conventions, national legislation, space faring nation, space law.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11881400 New Class of Chaotic Mappings in Symbol Space
Authors: Inese Bula
Abstract:
Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.
Keywords: Infinite symbol space, prefix metric, chaotic mapping, generator function, jump mapping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15061399 Time Map
Authors: A. Peveri
Abstract:
The interaction of mass will determine the curvature of space-time, may determine that events proceed at different rates of time at each point in space, so each has a corresponding gravitational potential time. So we can find different values of gravity (g), corresponding to different times (t), thus making a "map of time in space." The space-time is curved by present mass, causing a force of attraction towards the body, but if you invest the curvature of space-time, we find that this field is repulsive: Obtaining negative gravitational forces and positive gravitational forces respectively.
Keywords: Space-time, time, positive gravitation, negative gravitation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15101398 Weighted Composition Operators Acting between Kind of Weighted Bergman-Type Spaces and the Bers-Type Space
Authors: Amnah E. Shammahy
Abstract:
In this paper, we study the boundedness and compactness of the weighted composition operator Wu,φ, which is induced by an holomorphic function u and holomorphic self-map φ, acting between the NK-space and the Bers-type space H∞α on the unit disk.
Keywords: Weighted composition operators, NK-space, Bers-type space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16221397 Analysis on the Development and Evolution of China's Territorial Spatial Planning
Authors: He YuanYan
Abstract:
In recent years, China has implemented the reform of land and space planning. As an important public policy, land and space planning plays a vital role in the construction and development of cities. Land and space planning throughout the country is in full swing, but there are still many disputes from all walks of life. The content, scope, and specific implementation process of land and space planning are also ambiguous, leading to the integration of multiple regulation problems such as unclear authority, unclear responsibilities, and poor planning results during the implementation of land and space planning. Therefore, it is necessary to sort out the development and evolution of domestic and foreign land space planning, clarify the problems and cruxes from the current situation of China's land space planning, and sort out the obstacles and countermeasures to the implementation of this policy, so as to deepen the understanding of the connotation of land space planning. It is of great practical significance for all planners to correctly understand and clarify the specific contents and methods of land space planning and to smoothly promote the implementation of land space planning at all levels.
Keywords: Territorial spatial planning, public policy, land space, overall planning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2021396 Research on Spatial Morphology and Protection of Traditional Rural Settlements Based on Space Syntax: Taking Xiazhuang Village and Shijia Village in Huzhou as Example
Authors: Shenpu Liu
Abstract:
Space syntax, a paradigm of the urban research, which manifests people’s intuitive and abstract perception of a material space with a solid mathematical way, explores how space represents its social characteristics. Taking Xiazhuang village and Shijia Village in Huzhou as an example and focusing on inward structure and street space, this article recognizes the connotative significance of the settlement with the aid of space syntax theory and quantitative analysis method from the perspective of spatial configuration to present relevant suggestions for its future planning and provides references for traditional rural settlement protection.Keywords: Shijia village, space configuration, space syntax, traditional rural settlement, Xiazhuang village.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10221395 Topological Quantum Diffeomorphisms in Field Theory and the Spectrum of the Space-Time
Authors: Francisco Bulnes
Abstract:
Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, spectrum of ring, topological quantum diffeomorphisms.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9921394 Digital Transformation as the Subject of the Knowledge Model of the Discursive Space
Authors: Rafal Maciag
Abstract:
Due to the development of the current civilization, one must create suitable models of its pervasive massive phenomena. Such a phenomenon is the digital transformation, which has a substantial number of disciplined, methodical interpretations forming the diversified reflection. This reflection could be understood pragmatically as the current temporal, a local differential state of knowledge. The model of the discursive space is proposed as a model for the analysis and description of this knowledge. Discursive space is understood as an autonomous multidimensional space where separate discourses traverse specific trajectories of what can be presented in multidimensional parallel coordinate system. Discursive space built on the world of facts preserves the complex character of that world. Digital transformation as a discursive space has a relativistic character that means that at the same time, it is created by the dynamic discourses and these discourses are molded by the shape of this space.
Keywords: Knowledge, digital transformation, discourse, discursive space, complexity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6351393 A Proposal for U-City (Smart City) Service Method Using Real-Time Digital Map
Authors: SangWon Han, MuWook Pyeon, Sujung Moon, DaeKyo Seo
Abstract:
Recently, technologies based on three-dimensional (3D) space information are being developed and quality of life is improving as a result. Research on real-time digital map (RDM) is being conducted now to provide 3D space information. RDM is a service that creates and supplies 3D space information in real time based on location/shape detection. Research subjects on RDM include the construction of 3D space information with matching image data, complementing the weaknesses of image acquisition using multi-source data, and data collection methods using big data. Using RDM will be effective for space analysis using 3D space information in a U-City and for other space information utilization technologies.
Keywords: RDM, multi-source data, big data, U-City.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7991392 Fundamental Groups in Chaotic Flat Space and Its Retractions
Authors: A. E. El-Ahmady, M. Abu-Saleem
Abstract:
The purpose of this paper is to give a combinatorial characterization and construct representations of the chaotic fundamental groups of the chaotic submanifolds of chaotic flat space by using some geometrical transformations. The chaotic homotopy groups of the limit folding for chaotic flat space are presented. The chaotic fundamental groups of some types of chaotic geodesics in chaotic flat space are deduced.
Keywords: Chaotic flat space, Chaotic folding, Chaotic retractions, Chaotic fundamental groups.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1521