Refinements of some Hardy-Littlewood-Polya type inequalities and related results

Abstract

In this paper, we use an identity of Fink and present some interesting identities and inequalities for real valued functions and r-convex functions respectively. We also obtain refinements of some Hardy-Littlewood-Polya type inequalities. In addition, we use the Cebysev functional and the Gruss type inequalities and find the bounds for the remainder in the obtained identities. Finally, we present an interesting result related to the Ostrowski type inequalities.