Multiple Objective Programming Involving Differentiable (Hp, r)-invex Functions

in this paper, we introduce new types of generalized convex functions which include locally (hp, r)-pre-invex functions and (hp, r)-invex functions. relationship between these two new classes of functions are established. we also present the conditions for optimality in differentiable mathematical programming problems where the functions considered are (hp, r)-invex functions introduced in this paper.