On Semi‐(B, G)‐Preinvex Functions

We firstly construct a concrete semi-invex set which isnot invex. Basing on concept of semi-invex set, we introduce some kindsof 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 newgeneralized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining tocommon generalized convexity, we obtain results for our new generalizedconvexities. We extend the existing results in the literature