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

Ahmet Ocak Akdemir,Maria Alessandra Ragusa,Saad Ihsan Butt,Muhammad Nadeem

doi:10.3390/math9020122

Abstract

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.

Highlights

The existence of fractional analysis and the definition of new fractional integral and derivative operators revealed a similar situation for the inequality theory
Many inequalities have been generalized with the help of fractional integral operators and led to the construction of new approaches
The following new result have been given by Set et al for Chebyshev type inequalities via conformable integrals and generalized fractional integral operators

Summary

Introduction

The existence of fractional analysis and the definition of new fractional integral and derivative operators revealed a similar situation for the inequality theory. Many inequalities have been generalized with the help of fractional integral operators and led to the construction of new approaches (see the papers [13,14,15,16,17,18,19,20,21,22,23]). Some important special cases of the integral operators that is defined in Definition 3 can be concluded as: i

Results

Conclusion