On Semi- ( B , G ) -Preinvex Functions

Abstract

We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-$(B,G)$-preinvex functions, strictly semi-$(B,G)$-preinvex functions and explicitly semi-$(B,G)$-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.