Set Valued Equilibrium Problems Without Linear Structure

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED Set-Valued and Variational Analysis Pub Date : 2024-03-18 DOI:10.1007/s11228-024-00710-w

Irene Benedetti, Anna Martellotti

引用次数: 0

Abstract

In this paper we give several existence results for solutions of equilibrium problems in topological spaces without linear structure. To this end we introduce a new concept of convexity for maps and multivalued maps in spaces without linear structure. The discussion on convexity is enriched with some example useful to compare the new conditions with the existing one in literature. Finally, we apply the existence results obtained to a Nash equilibrium problem and to a maximization of a binary relation.

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无线性结构的集值均衡问题

本文给出了无线性结构拓扑空间中平衡问题解的几个存在性结果。为此，我们为无线性结构空间中的映射和多值映射引入了一个新的凸性概念。在讨论凸性时，我们举了一些例子，用来比较新条件和现有文献中的条件。最后，我们将得到的存在性结果应用于纳什均衡问题和二元关系的最大化问题。

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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来源期刊

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.

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