New extensions of Chebyshev-Pólya-Szegö type inequalities via conformable integrals

Erhan Deniz; Ahmet Ocak Akdemir; Ebru Yüksel; Erhan Deniz; Ahmet Ocak Akdemir; Ebru Yüksel

doi:10.3934/math.2020066

AIMS Mathematics

2020, Volume 5, Issue 2: 956-965. doi: 10.3934/math.2020066

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New extensions of Chebyshev-Pólya-Szegö type inequalities via conformable integrals

1.
Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey
2.
Department of Mathematics, Faculty of Arts and Sciences, Ağrı İbrahim Çeçen University, Ağrı, Turkey

Received: 05 October 2019 Accepted: 10 December 2019 Published: 08 January 2020
MSC : 26A33, 26D10, 26D15

Recently, several papers related to integral inequalities involving various fractional integral operators have been presented. In this work, motivated essentially by the previous works, we prove some new Polya-Szegö inequalities via conformable fractional integral operator and use them to prove some new fractional Chebyshev type inequalities concerning the integral of the product of two functions and the product of two integrals which are improvement of the results in the paper [Ntouyas, S.K., Agarwal, P. and Tariboon, J., On Polya-Szegö and Chebyshev type inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal (see ^[9])].
- Chebyshev inequality,
- Polya-Szegö type inequalities,
- conformable fractional integrals
Citation: Erhan Deniz, Ahmet Ocak Akdemir, Ebru Yüksel. New extensions of Chebyshev-Pólya-Szegö type inequalities via conformable integrals[J]. AIMS Mathematics, 2020, 5(2): 956-965. doi: 10.3934/math.2020066

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Abstract

Recently, several papers related to integral inequalities involving various fractional integral operators have been presented. In this work, motivated essentially by the previous works, we prove some new Polya-Szegö inequalities via conformable fractional integral operator and use them to prove some new fractional Chebyshev type inequalities concerning the integral of the product of two functions and the product of two integrals which are improvement of the results in the paper [Ntouyas, S.K., Agarwal, P. and Tariboon, J., On Polya-Szegö and Chebyshev type inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal (see ^[9])].

References

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