α-PRE-E-CONVEX AND α-E-CONVEX FUNCTIONS WITH APPLICATIONS TO MATHEMATICAL PROGRAMMING

α-PRE-E-CONVEX AND α-E-CONVEX FUNCTIONS WITH APPLICATIONS TO MATHEMATICAL PROGRAMMING

Seema Meena, D. B. Ojha

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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-prepseudo- E-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 α- pre-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.

Keywords

E-convex function, α-pre-E-convex function, α-prepseudo-E-convex function, α-E-convex function, optimality conditions.