A Class of G-Semipreinvex Functions and Optimality

Abstract

A class of $G$-semipreinvex functions, which are some generalizations of the semipreinvex functions, and the $G$-convex functions, is introduced. Examples are given to show their relations among $G$-semipreinvex functions, semipreinvex functions and $G$-convex functions. Some characterizations of $G$-semipreinvex functions are also obtained, and some optimality results are given for a class of $G$-semipreinvex functions. Ours results improve and generalize some known results.