On fixed point approach to equilibrium problem
Le Dung Muu, Xuan Thanh Le
TL;DR
This paper explores the connection between fixed points of the Moreau proximal mapping and solutions to a broad class of equilibrium problems, under certain monotonicity and Lipschitz conditions.
Contribution
It establishes a relationship between fixed points of proximal mappings and equilibrium solutions, extending understanding in this area.
Findings
Identifies conditions linking proximal fixed points to equilibrium solutions
Provides a framework for analyzing various equilibrium problems
Enhances methods for solving equilibrium problems using fixed point theory
Abstract
The equilibrium problem defined by the Nikaid\^o-Isoda-Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others as special cases. This paper presents a picture for the relationship between the fixed points of the Moreau proximal mapping and the solutions of the equilibrium problem that satisfies some kinds of monotonicity and Lipschitz-type condition.
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