On Semi-(B,G)‎-Preinvex Functions

Abstract EN

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.