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, $\eta$-invex, $(F,G)$-invex,  
$c$-strongly convex, $ \varphi $-uniformly convex and superquadratic functions, respectively. 
Each $H$-invex function attains its global minimum at an $H$-stationary point.
For $H$-invex functions we prove Jensen, Sherman and
Hardy-Littlewood-Polya-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.