Riemann–Liouville Fractional Integral Inequalities for Generalized Harmonically Convex Fuzzy-Interval-Valued Functions

Abstract

The framework of fuzzy-interval-valued functions (FIVFs) is a generalization of interval-valued functions (IVF) and single-valued functions. To discuss convexity with these kinds of functions, in this article, we introduce and investigate the harmonically $$\mathsf{h}$$ h -convexity for FIVFs through fuzzy-order relation (FOR). Using this class of harmonically $$\mathsf{h}$$ h -convex FIVFs ($$\mathcal{H}-\mathsf{h}$$ H - h -convex FIVFs), we prove some Hermite–Hadamard (H⋅H) and Hermite–Hadamard–Fejér (H⋅H Fejér) type inequalities via fuzzy interval Riemann–Liouville fractional integral (FI Riemann–Liouville fractional integral). The concepts and techniques of this paper are refinements and generalizations of many results which are proved in the literature.

Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr-h-Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings

“…[9]. Using the Riemann-Liouville fractional integral operator, Khan et al [10] developed (H-H) inequalities in an expanded form for harmonically convex mappings in the context of fuzzy interval-valued setting. Shi et al [11] began by developing Hermite-Hadamard inequality results using h-convex and harmonically h-convex functions, and extended their own work to coordinated convex interval-valued functions (I.V.F .S ) through fractional integrals.…”