Inequalities of Chebyshev-P\'olya-Szeg\"o Type via Generalized Proportional Fractional Integral Operators

TL;DR

This paper establishes new inequalities of Chebyshev-Pólya-Szegő type using generalized proportional fractional integral operators, bridging fractional analysis and inequality theory with novel mathematical results.

Contribution

It introduces new Chebyshev-Pólya-Szegő inequalities derived via generalized proportional fractional integrals, expanding the tools available in inequality theory.

Findings

New Chebyshev-Pólya-Szegő inequalities established

Utilizes classical inequalities and Taylor expansion in proofs

Provides novel approaches to inequalities involving products of functions

Abstract

This study is an example of a solid connection between fractional analysis and inequality theory, and includes new inequalities of the P\'{o}lya-Szeg% \"{o}-Chebyshev type obtained with the help of Generalized Proportional Fractional integral operators. The results have been performed by using Generalized Proportional Fractional integral operators, some classical inequalities such as AM-GM inequality, Cauchy-Schwarz inequality and Taylor series expansion of exponential function. The findings give new approaches to some types of inequalities that have involving the product of two functions in inequality theory.