α-Pre-e-convex and α-e-convex functions with applications to mathematical programming

Abstract

In this paper, we establish a new class of E-convexity, namely α-pre-Econvexity. We define α-pre-E-convex function (need not E-convex function), α-prepseudoE-convex function and discuss some properties of α-pre-E-convex functions. We observe that the class of α-prepseudo-E-convex functions is more general than the class of αpre-E-convex functions. We also introduce the class of α-E-convex functions which we prove it is equivalent to the class of differentiable α-pre-E-convex functions. Optimality conditions of these functions in mathematical programming problem are obtained.