模态空间中单调ρ-无穷半群的公共定点

Fixed Point Theory and Applications Pub Date : 2020-11-09 DOI:10.1186/s13663-020-00684-y

Noureddine El Harmouchi, Karim Chaira, El Miloudi Marhrani

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引用次数: 0

摘要

本文考虑了单调ρ-无穷半群，并给出了公共定点的存在性和收敛性结果。首先，我们证明在均匀凸模态空间和模态空间中，公共定点集合是非空的。然后，我们引入一种迭代算法来逼近同一类半群的公共定点。

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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Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces

In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.

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来源期刊

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.