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Research Article | Open Access

On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals

Mehmet Eyüp Kiriş1, Miguel Vivas-Cortez2 ( ), Gözde Bayrak3, Tuğba Çınar3, Hüseyin Budak4
Department of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University, Afyonkarahisar, Türkiye
Pontificia Universidad Católica del Ecuador, Facultad de Ciencias Naturales y Exactas, Escuela de Ciencias Físicas y Matemáticas, Sede Quito, Ecuador
Afyon Kocatepe University Graduate School of Natural and Applied Sciences, Afyonkarahisar, Türkiye
Department of Mathematics, Faculty of Science and Arts, Dü zce University, Düzce, Türkiye
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Abstract

In this study, some new Hermite-Hadamard type inequalities for co-ordinated convex functions were obtained with the help of conformable fractional integrals. We have presented some remarks to give the relation between our results and earlier obtained results. Moreover, an identity for partial differentiable functions has been established. By using this equality and concept of co-ordinated convexity, we have proven a trapezoid type inequality for conformable fractional integrals.

Keywords

convex functionsco-ordinated convex mappingHermite-Hadamard inequalityconformable fractional integraltrapezoid type inequalities
CLC number: 26A33, 26A51, 26B25, 26D10, 26D15

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 10267-10288
DOI: 10.3934/math.2024502

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Cite this article:
Kiriş ME, Vivas-Cortez M, Bayrak G, et al. On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals. AIMS Mathematics, 2024, 9(4): 10267-10288. https://doi.org/10.3934/math.2024502

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Received: 20 December 2023
Revised: 07 February 2024
Accepted: 09 February 2024
Published: 15 April 2024
©2024 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)