Mathematics and Computer Science, Volume 1

3Some New Inequalities Via Extended Generalized Fractional Integral Operator for Chebyshev Functional

Bhagwat R. Yewale* and Deepak B. Pachpatte

Department of Mathematics, Dr. B. A. M. University, Aurangabad, Maharashtra, India

Abstract

In present article, we prove some integral inequalities for Chebyshev functional using extended generalized fractional operator. The result obtained in the case of differentiable as well as Lipschitz functions.

Keywords: Chebyshev functional, Integral inequalities, Extended generalized fractional integral operator

3.1 Introduction

In 1882, Chebyshev introduced the following inequality [13]:

Let be differentiable functions such that and

(3.1)

then

(3.2)

The constant is the best possible.

The functional (3.1) have large number of applications in the field of statistics and probability. Many researcher’s provided lot of integral inequalities related to this functional in their literature (see [9, 12, 14, 15]).

Integrals and derivatives of any positive ...