On h-convexity

Abstract We introduce a class of h-convex functions which generalize convex, s-convex, Godunova–Levin functions and P-functions. Namely, the h-convex function is defined as a non-negative function f : J → R which satisfies f ( α x + ( 1 − α ) y ) ⩽ h ( α ) f ( x ) + h ( 1 − α ) f ( y ) , where h is a non-negative function, α ∈ ( 0 , 1 ) and x , y ∈ J . Some properties of h-convex functions are discussed. Also, the Schur-type inequality is given.