An extension of the Hermite-Hadamard inequality for a power of a convex function-Reference-Cited by-同舟云学术

An extension of the Hermite-Hadamard inequality for a power of a convex function

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Sayyari Yamin¹,Dehghanian Mehdi¹,Park Choonkil²,Paokanta Siriluk³⁴

Affiliation:

1. Department of Mathematics, Sirjan University of Technology , Sirjan , Iran

2. Research Institute for Natural Sciences, Hanyang University , Seoul 04763 , Korea

3. School of Science, University of Phayao , Phayao 56000 , Thailand

4. Department of Mathematics, Research Institute for Natural Sciences, Hanyang University , Seoul 04763 , Korea

Abstract

Abstract In this article, we obtain an extension of the classical Hermite-Hadamard inequality for convex functions (concave functions) extending it to the power functions

[ f ( x ) ] n

{[f\left(x)]}^{n}

. Some related inequalities are also introduced. By applying those results in analysis, we obtain new upper and lower bounds for the error function.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0542/pdf

Reference11 articles.

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3. H. Budak, S. Khan, M. A. Ali, and Y. Chu, Refinements of quantum Hermite-Hadamard-type inequailities, Open Math. 19 (2021), no. 1, 724–734, DOI: https://doi.org/10.1515/math-2021-0029.

4. F. Chen, Extensions of the Hermite-Hadamard Inequality for convex functions via fractional integrals, J. Math. Inequal. 10 (2016), no. 1, 75–81, DOI: https://doi.org/10.7153/jmi-10-07.

5. M. Benbachir, M. Dahmane, and A. El Farissi, An extension of the Hermite-Hadamard inequality for convex symmetrized functions, Real Anal. Exchange 38 (2012/2013), no. 2, 467–474.

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