Vector Equilibrium Problems on Dense Sets

TL;DR

This paper establishes conditions for the existence of solutions to vector equilibrium problems in topological vector spaces, focusing on dense subsets rather than entire domains, with applications to vector optimization and variational inequalities.

Contribution

It introduces new sufficient conditions based on self segment-dense subsets for solving vector equilibrium problems, extending previous results.

Findings

Solutions exist under conditions on dense subsets

Applicable to vector optimization problems

Provides a new approach to vector variational inequalities

Abstract

In this paper we provide sufficient conditions that ensure the existence of the solution of some vector equilibrium problems in Hausdorff topological vector spaces ordered by a cone. The conditions that we consider are imposed not on the whole domain of the operators involved, but rather on a self segment-dense subset of it, a special type of dense subset. We apply the results obtained to vector optimization and vector variational inequalities.