A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

Moin-ud-Din Junjua, Ather Qayyum (), Arslan Munir, Hüseyin Budak, Muhammad Mohsen Saleem and Siti Suzlin Supadi
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Moin-ud-Din Junjua: School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
Ather Qayyum: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Arslan Munir: Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan
Hüseyin Budak: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Türkiye
Muhammad Mohsen Saleem: Department of Mathematics, Pakistan International College Jeddah, Jeddah 23342, Saudi Arabia
Siti Suzlin Supadi: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2024, vol. 12, issue 3, 1-14

Abstract: Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo–Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.

Keywords: exponential convex function; fractional integrals; Hölder’s inequality; power-mean inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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