On fixed point approach to equilibrium problem
arXiv:2104.13283
Abstract
The equilibrium problem defined by the Nikaidô-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.
14 pages