Constrained Ordered Equilibrium Problems

TL;DR

This paper introduces constrained ordered equilibrium problems, extending traditional equilibrium concepts by incorporating domain restrictions, and proves existence theorems using fixed point theorems in partially ordered Banach spaces.

Contribution

It develops the theory of constrained ordered equilibrium problems and establishes existence results using fixed point theorems in partially ordered Banach spaces.

Findings

Existence of solutions in constrained ordered equilibrium problems

Extension of equilibrium problem theory to restricted domains

Application of fixed point theorems in partially ordered spaces

Abstract

In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the constrained mappings in the given problems. For this reason, we introduce the concepts of constrained ordered equilibrium problems, that are useful extensions of ordered equilibrium problems and ordinary equilibrium problems. Then, by using some fixed point theorems on posets, we prove several theorems for existence of solutions to some constrained ordered equilibrium problems. In particular, we investigate the solvability of some constrained ordered equilibrium problems in some partially ordered Banach spaces.