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.
Citation: Da Shi, Ghulam Farid, Abd Elmotaleb A. M. A. Elamin, Wajida Akram, Abdullah A. Alahmari, B. A. Younis. Generalizations of some $ q $-integral inequalities of Hölder, Ostrowski and Grüss type[J]. AIMS Mathematics, 2023, 8(10): 23459-23471. doi: 10.3934/math.20231192
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.
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