LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities

Muhammad Bilal Khan,Safar M Alghamdi,Bahaaeldin Abdalla,Thabet Abdeljawad,Abd Allah A Mousa,Muhammad Aslam Noor

doi:10.3390/fractalfract5040243

Abstract

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex I-V-Fs) and to establish Hermite–Hadamard type inequalities for LR-preinvex I-V-Fs using partial order relation (≤p). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.

Highlights

Motivated and inspired by ongoing research work, we have introduced the new generalization of convex functions is known as LR-preinvex intervalvalued functions (I-V-Fs) using partial order relation
Motivated and inspired by existing research, we introduce a novel extension of convex functions called as LR-preinvex I-V-Fs utilizing partial order relation
The LR-preinvex I-V-Fs were explored in this paper, a novel family of preinvex functions

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Fractional calculus traces back to the seventeenth century, when G.W. Leibniz and the Marquis de l’Hospital first discussed semi-derivatives. The number of papers on the use of integral inequalities in mathematical analysis has increased exponentially Integral operators such as Riemann–Liouville, Caputo, Katugampola, and Caputo–Fabrizio have been constructed in recent years utilizing a variety of fractional-order operator definitions. Khan et al [27] recently used fuzzy order relation to establish a new class of convex. F-I-V-Fs known as (h1 , h2 )-convex F-I-V-Fs, as well as a novel version of the H ·H type inequality for (h1 , h2 )-convex F-I-V-Fs that incorporates the FI Riemann integral. Motivated and inspired by ongoing research work, we have introduced the new generalization of convex functions is known as LR-preinvex I-V-Fs using partial order relation. We have discussed the exceptional cases as applications of this study

Preliminaries

Interval Fractional Hermite–Hadamard Inequalities

Conclusions and Future Plan