Hermite-Hadamard and Simpson’s type of inequalities for first and second ordered derivatives using product of (h1, h2, s)-convex and m-convex function

Yasin, Sabir; Omar, Zurni; Misiran, Masnita

doi:10.47974/JIM-1488

Open Access Research Article

Hermite-Hadamard and Simpson’s type of inequalities for first and second ordered derivatives using product of (h1, h2, s)-convex and m-convex function

^*Sabir YasinCorresponding authorsabiryasin77@gmail.comDepartment of Mathematics and StatisticsSchool of Quantitative SciencesUniversiti Utara MalaysiaUUM Sintok, Kedah, 06010, MalaysiaView full profile → , Zurni OmarDepartment of Mathematics and StatisticsSchool of Quantitative SciencesUniversiti Utara MalaysiaUUM Sintok, Kedah, 06010, MalaysiaView full profile → , Masnita MisiranAffiliation 1Department of Mathematics and StatisticsSchool of Quantitative SciencesUniversiti Utara MalaysiaUUM Sintok, Kedah, 06010, MalaysiaAffiliation 2Centre for Testing, Measurement and AppraisalUniversiti Utara MalaysiaUUM Sintok, Kedah, 06010, MalaysiaView full profile →

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pp. 1733–1744Vol. 26Issue 8December 2023DOI: 10.47974/JIM-1488XML

Received:: 15 Jul 2021
Published Online:: 11 Oct 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1488
Pages:: 1733–1744

Abstract

This article is dedicated to find the extensions for Hermite-Hadamard (H-H) and Simpson’s type of inequalities. By combining multiple existing convex functions by placing specific restrictions on them is the most effective in many approaches to find a new convex function. Here, to find the new function (h1, h2, s)-Convex and m-Convex Function are used. Because of the product of two or even more convex functions does not necessarily have to be convex, we decided to investigate merging distinct convex functions. Combining more than two convex functions in a novel adaptive way advances to new applications in a range of disciplines, including mathematics and other fields. In this paper, some extensions for Hermite-Hadamard and Simpson’s inequalities is explored. The newly constructed extensions of these inequalities will be considered as the improvements and refinements of previously obtained results.

Keywords

Hermite-Hadamard (H-H)Simpson’s Inequality Convex Function

Subject Classifications

(2010) 26A5126A3326D1026D0726D2026E60

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