Certain Grüss type inequalities involving the generalized fractional integral operator

Guotao Wang,Praveen Agarwal,Mehar Chand

doi:10.1186/1029-242x-2014-147

Abstract

Abstract A remarkably large number of Grüss type fractional integral inequalities involving the special function have been investigated by many authors. Very recently, Kalla and Rao (Matematiche LXVI(1):57-64, 2011) gave two Grüss type inequalities involving the Saigo fractional integral operator. Using the same technique, in this paper, we establish certain new Grüss type fractional integral inequalities involving the Gauss hypergeometric function. Moreover, we also consider their relevances for other related known results. MSC: 26D10, 26A33.

Highlights

Introduction and preliminariesIn recent years, a number of inequalities involving the fractional operators have been considered by many authors
We define a fractional integral operator Ktα,β,η,δ associated with the Gauss hypergeometric function as follows
We discuss some results regarding the fractional integral operator Ktα,β,η,δ which have been used in the present work

Summary

Introduction

Introduction and preliminariesIn recent years, a number of inequalities involving the fractional operators (like ErdélyiKober, Riemann-Liouville, Saigo fractional integral operators etc.) have been considered by many authors (see, e.g., [ – ]; for very recent work, see [ ] and [ ]). Let f and g be two functions which are defined and integrable on [a, b]. Kalla and Rao [ ] gave two Grüss type inequalities involving the Saigo fractional integral operator. Throughout the present paper, we shall investigate a fractional integral over the space Cλ introduced in [ ] and defined as follows.

Results

Conclusion