On new Chebyshev inequalities via fractional operators (original) (raw)
On the weighted fractional integral inequalities for Chebyshev functionals
Advances in Difference Equations, 2021
The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a fractional generalized weighted fractional integral involving another function$\mathcal{G}$Gin the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev’s functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev’s functionals with certain choices of$\omega (\theta )$ω(θ)and$\mathcal{G}(\theta )$G(θ)as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann–Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev’s functionals with certain choices of$\omega...
Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators
Mathematics
Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev’s functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann–Liouville fractional and classical integrals.
Chebyshev type inequalities via generalized fractional conformable integrals
Journal of Inequalities and Applications, 2019
Our aim in this present paper is to establish several Chebyshev type inequalities involving generalized fractional conformable integral operator recently introduced by T.U. Khan and M.A. Khan (J. Comput. Appl. Math. 346:378–389, 2019). Also, we present Chebyshev type inequalities involving Riemann–Liouville type fractional conformable integral operators as a particular result of our main result.
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.
Conformable fractional integral inequalities of Chebyshev type
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018
A number of Chebyshev type inequalities involving various fractional integral operators have, recently, been presented. Here, motivated essentially by the earlier works and their applications in diverse research subjects, we aim to establish several Chebyshev type inequalities involving generalized new conformable fractional integral operator.
Journal of Inequalities and Applications
Fractional analysis, as a rapidly developing area, is a tool to bring new derivatives and integrals into the literature with the effort put forward by many researchers in recent years. The theory of inequalities is a subject of many mathematicians’ work in the last century and has contributed to other areas with its applications. Especially in recent years, these two fields, fractional analysis and inequality theory, have shown a synchronous development. Inequality studies have been carried out by using new operators revealed in the fractional analysis. In this paper, by combining two important concepts of these two areas we obtain new inequalities of Chebyshev–Polya–Szegö type by means of generalized fractional integral operators. Our results are concerned with the integral of the product of two functions and the product of two integrals. They improve the results in the paper (J. Math. Inequal. 10(2):491–504, 2016).
On Chebyshev Type Inequalities Using Generalized k-Fractional Integral Operator
Progress in Fractional Differentiation and Applications
In this paper, using generalized k-fractional integral operator (in terms of the Gauss hypergeometric function), we establish new results on generalized k-fractional integral inequalities by considering the extended Chebyshev functional in case of synchronous function and some other inequalities.
Certain Inequalities Using Saigo Fractional Integral Operator
The main objective of this paper is to establish some new results on fractional integral inequalities by considering the extended Chebyshev functional in the case of synchronous function. The result is concerned with some inequalities using one fractional parameter and two parameters.