Inequalities for H-invex functions with applications for uniformly convex and superquadratic functions

Abstract

In this paper, we introduce and study H-invex functions including the classes of convex, ?-invex, (F,G)-invex, c-strongly convex, ?-uniformly convex and superquadratic functions, respectively. Each Hinvex function attains its global minimum at an H-stationary point. For H-invex functions we prove Jensen, Sherman and Hardy-Littlewood-P?lya-Karamata type inequalities, respectively. We also analyze such inequalities when the control function H is convex. As applications, we give interpretations of the obtained results for uniformly convex and superquadratic functions, respectively.