New refinements of Chebyshev–Pólya–Szegö-type inequalities via generalized fractional integral operators

Saad Ihsan Butt, Ahmet Ocak Akdemir, Muhammad Yousaf Bhatti, Muhammad Nadeem
2020 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
more » ... 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). MSC: 26A33; 26D10; 26D15
doi:10.1186/s13660-020-02425-6 fatcat:65umw2ovmnhptomeeeywqjw72e