Quasi-equilibrium problems with generalized monotonicity

TL;DR

This paper introduces new existence results for quasi-equilibrium problems in infinite-dimensional spaces using generalized monotonicity, linking these concepts to solution sets of equilibrium and convex feasibility problems.

Contribution

It provides novel existence theorems for quasi-equilibrium problems based on generalized monotonicity in infinite-dimensional spaces.

Findings

Generalized monotonicity characterizes solution sets of equilibrium problems.

Pseudomonotonicity and upper sign property are related under certain conditions.

New existence results extend the theory of quasi-equilibrium problems.

Abstract

In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of solution sets of equilibrium problems and convex feasibility problems. Moreover, we show that the concept of pseudomonotonicity and upper sign property are related under suitable assumptions.