GENERALIZED CONVEX-FUNCTIONS AND VECTOR VARIATIONAL-INEQUALITIES

In this paper, (alpha, phi, Q)-invexity is introduced, where alpha: X x X --> int R+m, phi: X x X --> X, X is a Banach space, Q is a convex cone of R(m). This unifies the properties of many classes of functions, such as Q-convexity, pseudo-linearity, representation condition, null space condition, and V-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (alpha, phi, Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (alpha, phi, Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.