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Research Article | Open Access

Hermite–Hadamard type inequalities for harmonic-arithmetic extended ( s 1 , m 1 )- ( s 2 , m 2 ) coordinated convex functions

Chun-Ying He1, Aying Wan1( ), Bai-Ni Guo2,3( )
School of Mathematics and Statistics, Hulunbuir University, Hulunbuir 021008, Inner Mongolia, China
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
Independent researcher, Dallas, TX 75252-8024, USA
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Abstract

In this paper, the authors define the notion of harmonic-arithmetic extended ( s 1 , m 1 )- ( s 2 , m 2 ) coordinated convex functions, establish a new integral identity, present some new Hermite–Hadamard type integral inequalities for harmonic-arithmetic extended ( s 1 , m 1 )- ( s 2 , m 2 ) coordinated convex functions, and derive some known results.

Keywords

Hermite–Hadamard type integral inequalityharmonic-arithmetic extended (s1, m1)-(s2, m2) coordinated convex functionintegral identity
CLC number: 26A51, 26D15, 26D20, 26E60, 41A55

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 17027-17037
DOI: 10.3934/math.2023869

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Cite this article:
He C-Y, Wan A, Guo B-N. Hermite–Hadamard type inequalities for harmonic-arithmetic extended ( s 1 , m 1 )- ( s 2 , m 2 ) coordinated convex functions. AIMS Mathematics, 2023, 8(7): 17027-17037. https://doi.org/10.3934/math.2023869

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Received: 08 March 2023
Revised: 27 April 2023
Accepted: 09 May 2023
Published: 15 July 2023
©2023 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)