ON THE LEVEL SETS OF (,)-QUASICONVEX FUNCTIONS

Abstract

The aim of this paper is to show that the characteristic property of the real-valued quasiconvex functions to have convex level sets can be naturally extended in the class of (G,W)-quasiconvex functions, introduced by us in [5], which in particular contains the cone-quasiconvex vector-valued functions in the sense of Dinh The Luc [3].