Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 46-54
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0225

A version of the Hermite-Hadamard inequality for Quasi \(F-(h,g,m)\)-convex functions

Ghulam Farid\(^{1,*}\) and Josip Pečarić\(^{2}\)
\(^{1}\) Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
\(^{2}\) Croatian Academy of Sciences and Arts, Zagreb, Croatia

Copyright © 2024 Ghulam Farid and Josip Pečarić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: November 22, 2023 – Accepted: May 11, 2024 – Published: June 30, 2024

Abstract

This paper aims to present Hermite-Hadamard type inequalities for a new class of functions, which will be denoted by \(Q_m^{h,g}(F;I)\) an and called class of quasi \(F-(h,g;m)\)-convex functions defined on interval \(I\). Many well known classes of functions can be recaptured from this new quasi convexity in particular cases. Also, several publish results are obtained along with new kinds of inequalities.

Keywords:

Convex function; \((h,g;m)\)-convex function; Hermite-Hadamard inequality