Some new fractional Hermite-Hadamard type inequalities for functions with co-ordinated extended <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mrow> <mml:mfenced open="(" close=")"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mrow> </mml:math> -prequasiinvex mixed partial derivatives
Wedad Saleh, Abdelghani Lakhdari, Adem Kılıçman, Assia Frioui, Badreddine Meftah
Abstract
This article introduces extended (s, m)-prequasiinvex functions on coordinates, a new form of generalized convex function. Using a previously established identity, we derive new frac-tional Hermite-Hadamard type integral inequalities for functions whose mixed partial derivatives belong to this new class of functions. The obtained results generalize existing Hermite-Hadamard type inequalities and have numerous applications in mathematics and physics. To demonstrate the utility of our findings, we provide examples of applications to special means, such as arithmetic, harmonic and p-logarithmic means.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).