G-semipreinvexity and its applications

Abstract

In this paper, we introduce some new kinds of generalized convexity, which include (semistrict) G-semipreinvexity and (semistrict) G-semipreincavity. Moreover, we establish the relations with common generalized convexity, present properties of (semistrictly) G-semipreinvex and (semistrictly) G-semipreincave functions, and also give characterizations of the classes of G-semipreinvex and G-semipreincave functions. Moreover, we deal with programming involving G-semipreinvex functions. Our results extend the existing ones in the literature. Mathematics Subject Classification 90C26 · 90C46