Novel Analysis of Hermite–Hadamard Type Integral Inequalities via Generalized Exponential Type m -Convex Functions

Muhammad Tariq, Hijaz Ahmad, Clemente Cesarano, Hanaa Abu-Zinadah, Ahmed E. Abouelregal and Sameh Askar
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Muhammad Tariq: Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
Hijaz Ahmad: Information Technology Application and Research Center，Istanbul Ticaret University, 34840 Istanbul, Turkey
Clemente Cesarano: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Hanaa Abu-Zinadah: Department of Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Ahmed E. Abouelregal: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Sameh Askar: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2021, vol. 10, issue 1, 1-21

Abstract: The theory of convexity has a rich and paramount history and has been the interest of intense research for longer than a century in mathematics. It has not just fascinating and profound outcomes in different branches of engineering and mathematical sciences, it also has plenty of uses because of its geometrical interpretation and definition. It also provides numerical quadrature rules and tools for researchers to tackle and solve a wide class of related and unrelated problems. The main focus of this paper is to introduce and explore the concept of a new family of convex functions namely generalized exponential type m -convex functions. Further, to upgrade its numerical significance, we present some of its algebraic properties. Using the newly introduced definition, we investigate the novel version of Hermite–Hadamard type integral inequality. Furthermore, we establish some integral identities, and employing these identities, we present several new Hermite–Hadamard H–H type integral inequalities for generalized exponential type m -convex functions. These new results yield some generalizations of the prior results in the literature.

Keywords: convex function; Hölder’s inequality; power-mean integral inequality; m-type convexity; exponential convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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