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Research Article | Open Access

New Simpson type inequalities for twice differentiable functions via generalized fractional integrals

Xuexiao You1, Fatih Hezenci2, Hüseyin Budak2( ), Hasan Kara2
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
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Abstract

Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, Simpson type inequalities for twice differentiable functions are also investigated slightly. Hence, we establish a new identity for twice differentiable functions. Furthermore, by utilizing generalized fractional integrals, we prove several Simpson type inequalities for functions whose second derivatives in absolute value are convex.

Keywords

Simpson type inequalitiesgeneralized fractional integralsconvex functions
CLC number: 26A33, 26D07, 26D10, 26D15

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3959-3971
DOI: 10.3934/math.2022218

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Cite this article:
You X, Hezenci F, Budak H, et al. New Simpson type inequalities for twice differentiable functions via generalized fractional integrals. AIMS Mathematics, 2022, 7(3): 3959-3971. https://doi.org/10.3934/math.2022218

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Received: 26 October 2021
Accepted: 06 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)