Generalized convex function is a generalization of convex func-tion

including pseudoconvex function

quasiconvex function

r-convex function

etc.The properties and operation properties of generalized convex functionplay an imporant role in generalized convex programming.Xue Jiasheng discu-sed the constructive method of pseudoconvex function;J.P.Crouzeix dicussedthe properties of quasiconvex function.This paper only discusses a class ofgeneralized convex function

r-convex functions.