Some new estimates of generalized ( h 1 , h 2 ) -convex functions

Abstract

In this article, we introduce a new class of generalized convex functions involving two arbitrary auxiliary functions h1,h2:I=[a,b]⊆R→Rh1,h2:I=[a,b]⊆R→R, which is called generalized (h1,h2)(h1,h2) convex functions. We obtain several new classes of convex functions as special cases. We derive some new integral inequalities for generalized convex functions. Several special cases are also discussed. Results proved in this paper can be viewed as new significant contributions in this area.