Existence and Continuity of Solutions to Simultaneous Vector Equilibrium Problems

In this paper, we give the notion of a P-monotone family of mappings, an extension of a monotone family of functions introduced by Djafari Rouhani et al. [6]. Using a fixed point theorem, we prove the existence of solution of simultaneous vector equilibrium problem in Hausdroff topological vector space. Further, we give sufficient conditions for the upper semicontinuity of the solution set of the parametric problem corresponding to the simultaneous vector equilibrium problems. The theorems presented in this paper generalize and unify many important corresponding results in the literature.