Stability of approximate solution mappings for generalized Ky Fan inequality

Abstract

This paper is concerned with the stability for a generalized Ky Fan inequality when it is perturbed by vector-valued bifunction sequence and set sequence. By continuous convergence of the bifunction sequence and Painleve–Kuratowski convergence of the set sequence, we establish the Painleve–Kuratowski convergence of the approximate solution mappings of a family of perturbed problems to the corresponding solution mapping of the original problem. Our main results are new and different from the ones in the literature.