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).

中文翻译：

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Chebyshev-Pólya-Szegö型不等式通过广义分数积分算符的新改进

分数分析作为一个快速发展的领域，是近年来许多研究人员提出的努力，将新的导数和积分带入文献的工具。不平等理论是上个世纪许多数学家工作的主题，并在其应用方面为其他领域做出了贡献。尤其是近年来，分数分析和不等式理论这两个领域显示出同步发展。通过使用分数分析中揭示的新运算符，进行了不平等研究。在本文中，通过结合这两个领域的两个重要概念，我们借助于广义分数积分算子获得了新的Chebyshev-Polya-Szegö型不等式。我们的结果与两个函数的乘积和两个积分的乘积有关。