New Hermite–Hadamard Inequalities in Fuzzy-Interval Fractional Calculus and Related Inequalities

Abstract

It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this relation, firstly, we derive some discrete Jensen and Schur inequalities for convex fuzzy interval-valued functions (convex fuzzy-IVF), and then, we present Hermite–Hadamard inequalities (-inequalities) for convex fuzzy-IVF via fuzzy interval Riemann–Liouville fractional integrals. These outcomes are a generalization of a number of previously known results, and many new outcomes can be deduced as a result of appropriate parameter and real valued function selections. We hope that our fuzzy order relations results can be used to evaluate a number of mathematical problems related to real-world applications.

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

“…They demonstrated the validity of characterizations with help of examples, and improved the previous results provided by Li and Noor [27]. We refer to the readers for further analysis of literature on the applications and properties of variational-like inequalities and generalized convex fuzzy mappings, see [2,9,16,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] and the references therein.…”

“…Remark 5.2. The inequalities (44) and (48), shows that the variational-like inequalities arise naturally in connection with the minimization of the G-differentiable preinvex fuzzy mappings subject to certain constraints.…”

Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

“…Proof. Choosing α = 1 in Theorem 2 and using the same technique as in our demonstration of Proposition 1, we obtain the desired inequality (26). Remark 6.…”

“…The two-sided inequality (1) has become a very important foundation within the field of mathematical analysis and optimization. Several applications of inequalities of this type have been derived in a number of different settings (see [21][22][23][24][25][26][27][28][29]).…”

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

“…wherẽis a convex fuzzy-IVF. We urge the readers to [32][33][34][35][36][37][38][39][40][41][42] and the citations therein for further review of related literature on the implementations and characterization of fuzzy-interval, inequalities and generalized convex fuzzy mappings.…”