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

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 t...

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Bibliographic Details
Published in:	AIMS mathematics Vol. 8; no. 10; pp. 23459 - 23471
Main Authors:	Shi, Da, Farid, Ghulam, Elamin, Abd Elmotaleb A. M. A., Akram, Wajida, Alahmari, Abdullah A., Younis, B. A.
Format:	Journal Article
Language:	English
Published:	AIMS Press 01-01-2023
Subjects:	güss inequality hadamard inequality hölder inequality ostrowski inequality q $-$ h $-integral q $-integral
Online Access:	Get full text
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Summary:	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.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.20231192