Integral inequalities of Hermite-Hadamard type via $ q-h $ integrals-Reference-Cited by-同舟云学术

Integral inequalities of Hermite-Hadamard type via $ q-h $ integrals

Published:2023 Issue:7 Volume:8 Page:16165-16174
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Chen Dong¹²,Anwar Matloob³,Farid Ghulam⁴,Bibi Waseela⁴

Affiliation:

1. School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, China

2. Key Laboratory of Pattern Recognition and Intelligent Information Processing of Sichuan, Chengdu University, Chengdu, China

3. School of Natural Sciences, NUST, Islamabad, Pakistan

4. Department of Mathematics, COMSATS Islamabad, Attock Campus, Pakistan

Abstract

<abstract><p>The well-known Hermite-Hadamard inequality for convex functions is extensively studied for different kinds of integrals and derivatives. This paper investigates some of its variants for $ q-h $-integrals using properties of convex functions. Inequalities for $ q $-integrals that have been published in recent years can be extracted from the main results of this paper.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference16 articles.

1. M. Z. Sarikaya, E. Set, H. Yaldiz, N. Başak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013), 2403–2407. https://doi.org/10.1016/j.mcm.2011.12.048

2. M. Andrić, G. Farid, J. Pečarić, Analytical inequalities for fractional calculus operators and the Mittag-Leffler function, Zagreb: Element, 2021.

3. N. Alp, M. Z. Sarikaya, M. Kunt, I. Iscan, $q$-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 30 (2018), 193–203. https://doi.org/10.1016/j.jksus.2016.09.007

4. S. Bermudo, P. Kórus, J. E. Nápoles Valdés, On $q$-Hermite–Hadamard inequalities for general convex functions, Acta Math. Hungar., 162 (2020), 364–374. https://doi.org/10.1007/s10474-020-01025-6

5. M. A. Khan, N. Mohammad, E. R. Nwaeze, Y.-M. Chu, Quantum Hermite–Hadamard inequality by means of a Green function, Adv. Differ. Equ., 2020 (2020), 99. https://doi.org/10.1186/s13662-020-02559-3