On some generalization of Wright-convex functions

In the present paper we introduce a notion of γ -convexity which is a common generalization of the notion of convexity, Wright-convexity, strong convexity and many others. We introduce a notion of γ -derivative which is connected to γ -convex functions and we examine its properties. In the last section of the paper we give conditions which assure the continuity of an arbitrary γ -convex function.