Applications of Hölder-İşcan inequality for $ n $-times differentiable $ (s, m) $-convex functions

Khuram Ali Khan; Shaista Ayaz; İmdat İşcan; Nehad Ali Shah; Wajaree Weera; Khuram Ali Khan; Shaista Ayaz; İmdat İşcan; Nehad Ali Shah; Wajaree Weera

doi:10.3934/math.2023082

AIMS Mathematics

2023, Volume 8, Issue 1: 1620-1635. doi: 10.3934/math.2023082

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Research article

Applications of Hölder-İşcan inequality for $ n $-times differentiable $ (s, m) $-convex functions

1.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
2.
Government Associate College for Women, Fateh Pur, Layyah, Pakistan
3.
Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Turkey
4.
Department of Mechanical Engineering, Sejong University, Seoul, 05006, South Korea
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
^† These authors contributed equally to this work and are co-first authors

Received: 18 August 2022 Revised: 08 October 2022 Accepted: 10 October 2022 Published: 24 October 2022
MSC : 26D07, 26D15, 26E70

In this work, Hölder-Isçan inequality is used for the class of $ n $-times differentiable $ (s, m) $-convex functions. The outcomes are new Hermite-Hadamard type inequalities and modified integrals are estimated by better bounds. Special cases are deduced as the existing results from literature. Furthermore, some applications to arithmetic, geometric and logarithmic means are also presented.
- $ (s, m) $-convex function,
- $ n $-times differentiable functions,
- Hermite-Hadamard inequalities,
- Hölder-Isçan inequality,
- means
Citation: Khuram Ali Khan, Shaista Ayaz, İmdat İşcan, Nehad Ali Shah, Wajaree Weera. Applications of Hölder-İşcan inequality for $ n $-times differentiable $ (s, m) $-convex functions[J]. AIMS Mathematics, 2023, 8(1): 1620-1635. doi: 10.3934/math.2023082

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Abstract

In this work, Hölder-Isçan inequality is used for the class of $ n $-times differentiable $ (s, m) $-convex functions. The outcomes are new Hermite-Hadamard type inequalities and modified integrals are estimated by better bounds. Special cases are deduced as the existing results from literature. Furthermore, some applications to arithmetic, geometric and logarithmic means are also presented.

References

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