Between quasi-convex and convex set-valued mappings

Abstract. The aim of this paper is to give sufficient conditions for a quasiconvex setvalued mapping to be convex. In particular, we recover several known characterizations of convex real-valued functions, given in terms of quasiconvexity and Jensen-type convexity by K. Nikodem [1], F.A. Behringer [2], and X.M. Yang, K.L. Teo and X.Q. Yang [3].

• Type: Journal
• Year: 2004
• Where: APPML
• Authors: J. Benoist, N. Popovici
• Keywords: APPML 2004, Convex Real-valued Functions, Jensen-type Convexity, Sufficient Conditions