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Research Article | Open Access

Generalizations of some q-integral inequalities of Hölder, Ostrowski and Grüss type

Da Shi1, Ghulam Farid2( ), Abd Elmotaleb A. M. A. Elamin3, Wajida Akram2, Abdullah A. Alahmari4, B. A. Younis5
School of Computer Science, Chengdu University, Chengdu, China
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
Department of Mathematics, College of Science and Humanity, Prince Sattam bin Abdulaziz University, Sulail, Saudi Arabia
Department of Mathematical Sciences, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
King Khalid University, College of Arts & Sciences, Saudi Arabia
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Abstract

This paper investigates some well-known inequalities for q- h-integrals. These include Hölder, Ostrowski, Grüss and Opial type inequalities. Refinement of the Hadamard inequality for q- h-integrals is also established by applying the definition of strongly convex functions. From main theorems, q-Hölder, q-Ostrowski and q-Grüss inequalities can be obtained in particular cases.

Keywords

q-integralq-h-integralHölder inequalityOstrowski inequalityGüss inequalityHadamard inequality
CLC number: 26A51, 26A33, 33E12

References

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 23459-23471
DOI: 10.3934/math.20231192

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Cite this article:
Shi D, Farid G, Elamin AEAMA, et al. Generalizations of some q-integral inequalities of Hölder, Ostrowski and Grüss type. AIMS Mathematics, 2023, 8(10): 23459-23471. https://doi.org/10.3934/math.20231192

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Received: 25 April 2023
Revised: 06 June 2023
Accepted: 15 June 2023
Published: 15 October 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)