Extended Hermite–Hadamard inequalities

Lakhlifa Sadek; Ali Algefary; Lakhlifa Sadek; Ali Algefary

doi:10.3934/math.20241709

AIMS Mathematics

2024, Volume 9, Issue 12: 36031-36046. doi: 10.3934/math.20241709

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Research article

Extended Hermite–Hadamard inequalities

Lakhlifa Sadek ^{1,2
,
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Ali Algefary ^{3
,
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1.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamilnadu, India
2.
Department of Mathematics, Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Tetouan, Morocco
3.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Received: 17 November 2024 Revised: 17 December 2024 Accepted: 19 December 2024 Published: 26 December 2024
MSC : 26A33, 46N10, 46N20

In this manuscript, we formulated Hermite–Hadamard inequalities for convex functions by employing cotangent integrals. Additionally, we extended these Hermite–Hadamard inequalities to encompass cotangent integrals and give the application.
- fractional derivatives,
- cotangent integral operators,
- confluent hypergeometric function,
- Hermite–Hadamard inequalities,
- optimization
Citation: Lakhlifa Sadek, Ali Algefary. Extended Hermite–Hadamard inequalities[J]. AIMS Mathematics, 2024, 9(12): 36031-36046. doi: 10.3934/math.20241709

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Abstract

In this manuscript, we formulated Hermite–Hadamard inequalities for convex functions by employing cotangent integrals. Additionally, we extended these Hermite–Hadamard inequalities to encompass cotangent integrals and give the application.

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