On Chebyshev Type Inequalities Using Generalized k-Fractional Integral Operator (original) (raw)

Grüss Type k-Fractional Integral Operator Inequalities and Allied Results

International Journal of Analysis and Applications, 2023

This paper aims to derive fractional Grüss type integral inequalities for generalized kfractional integral operators with Mittag-Leffler function in the kernel. Many new results can be deduced for several integral operators by giving specific values to the parameters involved in Mittag-Leffler function. Moreover, the results of this paper reproduce a lot of already published results.

On Fractional Integral Inequalities Involving Hypergeometric Operators

Chinese Journal of Mathematics, 2014

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

Certain Grüss type inequalities involving the generalized fractional integral operator

Journal of Inequalities and Applications, 2014

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

On New Generalized Fractional Integral Operators and Related Fractional Inequalities

2020

In this paper, we define the generalized kkk-fractional integrals of a function with respect to the another function which generalizes many different types of fractional integrals such as Riemann-Liouville fractional, Hadamard fractional integrals, Katugampola fractional integral, (k,s)(k,s)(k,s)-fractional integral operators. Moreover, we obtain Hermite-Hadamard inequalities utilizing kkk-fractional integrals of a function with respect to the another function. We also investigate trapezoid inequalities for the functions whose derivatives in absolute value are convex. Finally, some special cases of these inequalities are given.

Chebyshev-Grüss Type Inequalities for Hadamard \(k\)-Fractional Integrals

Communications in Mathematics and Applications, 2018

Integral inequalities are taken up to be important as they are useful in the study of different classes of differential and integral equations. During the past several years, many researchers have obtained various fractional integral inequalities comprising the different fractional differential and integral operators. A considerable work is done associated with classical and variants of Gruss type inequality, which actually connects the integral of the product of two functions with the product of their integrals. In this paper, we present the Chebyshev-Gruss type inequalities for Hadamard fractional integrals in the framework of parameter \(k > 0\).

Certain inequalities associated with Hadamard k-fractional integral operators

Journal of Inequalities and Applications, 2016

We aim to present some new Pólya-Szegö type inequalities associated with Hadamard k-fractional integral operators, which are also used to derive some Chebyshev type integral inequalities. Further we apply some of the results presented here to a function which is bounded by the Heaviside functions.

New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Mathematics

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.