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

Da Shi; Ghulam Farid; Abd Elmotaleb A.M.A. Elamin; Wajida Akram; Abdullah A. Alahmari; B. A. Younis

doi:10.3934/math.20231192

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

Da Shi
, Ghulam Farid
, Abd Elmotaleb A.M.A. Elamin
, Wajida Akram
, Abdullah A. Alahmari
, B. A. Younis

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	23459-23471
Number of pages	13
Journal	AIMS Mathematics
Volume	8
Issue number	10
DOIs	https://doi.org/10.3934/math.20231192
State	Published - 2023

Keywords

Güss inequality
Hadamard inequality
Hölder inequality
Ostrowski inequality
q-h-integral
q-integral

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10.3934/math.20231192

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title = "Generalizations of some q-integral inequalities of H{\"o}lder, Ostrowski and Gr{\"u}ss type",

abstract = "This paper investigates some well-known inequalities for q-h-integrals. These include H{\"o}lder, Ostrowski, Gr{\"u}ss 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-H{\"o}lder, q-Ostrowski and q-Gr{\"u}ss inequalities can be obtained in particular cases.",

keywords = "G{\"u}ss inequality, Hadamard inequality, H{\"o}lder inequality, Ostrowski inequality, q-h-integral, q-integral",

author = "Da Shi and Ghulam Farid and Elamin, \{Abd Elmotaleb A.M.A.\} and Wajida Akram and Alahmari, \{Abdullah A.\} and Younis, \{B. A.\}",

note = "Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press.",

year = "2023",

doi = "10.3934/math.20231192",

language = "English",

volume = "8",

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T1 - Generalizations of some q-integral inequalities of Hölder, Ostrowski and Grüss type

AU - Shi, Da

AU - Farid, Ghulam

AU - Elamin, Abd Elmotaleb A.M.A.

AU - Akram, Wajida

AU - Alahmari, Abdullah A.

AU - Younis, B. A.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Güss inequality

KW - Hadamard inequality

KW - Hölder inequality

KW - Ostrowski inequality

KW - q-h-integral

KW - q-integral

UR - https://www.scopus.com/pages/publications/85166004186

U2 - 10.3934/math.20231192

DO - 10.3934/math.20231192

M3 - Article

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SN - 2473-6988

VL - 8

SP - 23459

EP - 23471

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 10

ER -

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

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Keywords

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