Searching a solution of an equilibrium problem in the range of a set-valued mapping
Optimization Eruditorum, Volume 3, Issue 2, August 2026, Pages 66–74
MIRCEA BALAJ
Department of Mathematics, University of Oradea, Romania
Abstract
If \(X\) is a nonempty set and \(f\) is a real bifunction defined on \(X \times X\), the problem of finding \(x_0 \in X\) such that \(f(x_0, y) \geq 0\) for all \(y \in X\), is called an equilibrium problem. In this paper, we study the existence of a solution to the equilibrium problem that belongs to the range of a given set-valued mapping. For this purpose we need to introduce the concept of bifunction diagonally quasiconvex with respect to a set-valued mapping. The proposed problem is studied first in the general case, and then for special types of equilibrium problems (namely, minimum optimization problems, respectively variational inequalities).
Cite this Article as
Mircea Balaj, Searching a solution of an equilibrium problem in the range of a set-valued mapping, Optimization Eruditorum, 3(2), 66–74, 2026