r-convex functions

A family of real functions, calledr-convex functions, which represents a generalization of the notion of convexity is introduced. This family properly includes the family of convex functions and is included in the family of quasiconvex functions. Some properties ofr-convex functions are derived and relations with other generalizations of convex functions are discussed.Portions of this paper were presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands.Research for this paper was supported in part by the Gerard Swope Fund at the Technion.