On Some Characterizations of Sub-b-s-Convex Functions

Abstract

In the present paper, a class of generalized convex functions, called sub-b-s-convex functions, is introduced by modulating the definitions of s-convex functions and sub-b-convex functions. In order to study the basic properties of sub-b-s-convex functions in both general case and differentiable case, the sub-b-s-convex set is presented. As applications, the sufficient conditions of optimality for both unconstrained and inequality constrained programming are also obtained under the sub-b-s-convexity.