Existence of weak efficient solutions in set-valued equilibrium problems
Optimization Eruditorum, Volume 3, Issue 2, August 2026, Pages 127–137
NASIR HUSSAIN
Department of Mathematics, Shibli National College, Azamgarh, 276001, India
MONIRUL ISLAM
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
Abstract
In this paper, we consider the set-valued equilibrium problems and study the existence of weak efficient solutions in Hausdorff topological vector space. By using generalized convexity for setvalued maps, we study existence results for weak efficient solutions to set-valued equilibrium problems with or without nonlinear scalarization techniques. We introduce the notion of the negative transitivity property for set-valued maps. By using the nonlinear scalarization techniques, we establish the existence of the solutions in set-valued equilibrium problems when the involved set-valued maps have a negative transitivity property. As an application, we apply our results to non-cooperative game theory.
Cite this Article as
Nasir hussain and monirul islam, Existence of weak efficient solutions in set-valued equilibrium problems, Optimization Eruditorum, 3(2), 127–137, 2026