Vector equilibrium problems for multifunctions in topological semilattice spaces

Abstract

Abstract. Let K be a nonempty compact ∆-convex subset of a topological semilattice with pathconnected intervals. In this paper, under new assumptions, we establish some existence theorems ofis the set of all fixed points of the multifunction A : K → 2 K and V EP (f ) is the set of all solutions for the vector equilibrium problems of the multifunction f from K × K to a topological vector space Y . These results generalize and improve the recent ones in the literature. Some examples are given to illustrate our results.