Abstract. Generalizing the notions of Jensen and Wright convexity, we introduce the concept of $(M;p,q)$-convexity. Our main results show that, under continuity assumptions, $(M;p,q)$-convexity is equivalent to convexity.

AMS Subject Classification (1991): 26B25, 26D15, 39B62

Received September 6, 2004. (Registered under 5860/2009.)