关于相对非扩张映射和最佳邻近对的推广

Fixed Point Theory and Applications Pub Date : 2023-11-27 DOI:10.1186/s13663-023-00754-x

Karim Chaira, Belkassem Seddoug

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引用次数: 0

摘要

设A和B是赋范空间X的两个非空子集，并设$T: A \cup B \到A \cup B$是一个循环(正则表达式)。(非循环)映射。本文的目的是在T上建立保证其相对非扩张性的弱条件。这个想法是为了恢复Matkowski (Banach J. Math)在两篇论文中提到的结果。植物学报，2007;[j] .不动点理论，24(7)，2022)，用一个循环(循环)代替非膨胀映射$f: C \到C$。(非循环)相对非扩展映射，以获得最佳邻近对。此外，我们还提供了一个函数方程的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On a generalization of a relatively nonexpansive mapping and best proximity pair

Let A and B be two nonempty subsets of a normed space X, and let $T: A \cup B \to A \cup B$ be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping $f: C \to C$ with a cyclic (resp., noncyclic) relatively nonexpansive mapping to obtain the best proximity pair. Additionally, we provide an application to a functional equation.

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.