On some generalization of Wright-convex functions

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