Generalized \(m\)-preinvexity on fractal set and related local fractional integral inequalities with applications

Volume 30, Issue 4, pp 352--371 http://dx.doi.org/10.22436/jmcs.030.04.05

Publication Date: February 18, 2023 Submission Date: January 08, 2023 Revision Date: January 15, 2023 Accteptance Date: January 30, 2023

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Authors

S. Al-Sa'di - Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan. M. Bibi - Department of Basics Sciences, University of Engineering and Technology, Taxila, Pakistan. M. Muddassar - Department of Basics Sciences, University of Engineering and Technology, Taxila, Pakistan. S. Kermausuor - Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL, 36101, USA.

Abstract

In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate the current initiated idea. Furthermore, we prove the latest variant of Hermite-Hadamard type inequality employing the proposed definition of preinvexity. We also derive several novel versions of inequalities of the Hermite-Hadamard type and Fejér-Hermite-Hadamard type for the first-order local differentiable generalized \(m\)-preinvex functions. Finally, some new inequalities for the generalized means and generalized random variables are established as applications.

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Keywords

• Generalized \(m\)-preinvex functions
• generalized Hermite-Hadamard inequality
• generalized Fejér-Hermite-Hadamard type inequality
• fractal sets
• fractional integral inequalities

MSC

•  26D10
•  26D15
•  26A33
•  26A51

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