On strongly $h$-convex functions

Abstract

‎We introduce the notion of strongly $h$-convex functions (defined on‎ ‎a normed space) and present some properties and representations of‎ ‎such functions‎. ‎We obtain a characterization of inner product spaces‎ ‎involving the notion of strongly $h$-convex functions‎. ‎Finally‎, ‎a‎ ‎Hermite-Hadamard-type inequality for strongly $h$-convex functions‎ ‎is given‎.