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

Journal of inequalities and applications

article

Saad Ihsan Butt¹  Ahmet Ocak Akdemir²  Muhammad Yousaf Bhatti¹  Muhammad Nadeem¹ 

[1] COMSATS University Islamabad, Lahore Campus;Department of Mathematics, Faculty of Arts and Sciences, Ağrı İbrahim Çeçen University

关键词: Chebyshev inequality;    Polya–Szegö type inequalities;    Generalized fractional integrals;   

DOI  :  10.1186/s13660-020-02425-6

学科分类：电力

来源: SpringerOpen

【 摘 要 】

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).

【 授权许可】

CC BY