A Ky Fan minimax inequality for quasiequilibria on finite dimensional spaces

TL;DR

This paper establishes new existence results for quasiequilibrium problems in finite-dimensional spaces using a Ky Fan minimax inequality approach, extending classical equilibrium theory to more general settings.

Contribution

It introduces a Ky Fan minimax inequality framework for quasiequilibria, providing verifiable conditions and extending classical results to broader cases.

Findings

Existence of solutions under new conditions

Reduction to classical equilibrium problems in special cases

Comparison with existing literature results

Abstract

Several results concerning existence of solutions of a quasiequilibrium problem defined on a finite dimensional space are established. The proof of the first result is based on a Michael selection theorem for lower semicontinuous set-valued maps which holds in finite dimensional spaces. Furthermore this result allows one to locate the position of a solution. Sufficient conditions, which are easier to verify, may be obtained by imposing restrictions either on the domain or on the bifunction. These facts make it possible to yield various existence results which reduce to the well known Ky Fan minimax inequality when the constraint map is constant and the quasiequilibrium problem coincides with an equilibrium problem. Lastly, a comparison with other results from the literature is discussed.