CLOSEDNESS OF SET OF EFFICIENT SOLUTIONS FOR GENERALIZED KY FAN INEQUALITY PROBLEMS

Abstract

In this paper, we discuss the closedness of set of efficient solutions for generalized Ky Fan inequality problems in topological vector spaces. We introduce a concept of section mapping of a bifunction. By using the lower semicontinuity of the section mapping, we present sufficient conditions for the closedness of set of efficient solutions to the generalized Ky Fan inequality problems. We give conditions to guarantee the lower semicontinuity of the section mapping. We give also an example to illustrate that the condition of the lower semicontinuity of the section mapping is essential for the closedness of set of efficient solutions for generalized Ky Fan inequality problems. As an application, we give results of closedness of set of efficient solutions for vector optimization problems and for Lipschitz vector variational inequalities.