New Hermite–Hadamard-type inequalities for "Equation missing"-convex fuzzy-interval-valued functions

Khan, Muhammad Bilal; Noor, Muhammad Aslam; Noor, Khalida İnayat; Chu, Yu‐Ming

doi:10.1186/s13662-021-03245-8

Cited by 70 publications

(21 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to the vast applications of convexity and fractional HH-inequality in mathematical analysis and optimization, many authors have discussed the applications, refinements, generalizations, and extensions, see [27][28][29][30][31][32][33][34][35][36][37][38] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…and , ς) and 1 = ς and χ(s) = s, then from (31) and (36) one achieves coming inequality given in [27]:…”

Section: 𝜉 ≼ 𝜛 If and Only If [𝜉] ≤ [𝜛]mentioning

confidence: 78%

“…Khan et al [24][25][26][27] extended the class of convex F•Ms and defined h-convex and (h 1 , h 2 )-convex F-IV-Fs using fuzzy partial order relation. Moreover, they introduced H.H, Hermite-Hadamard-Fejér (H.H Fejér), fractional H.H and H.H Fejér for h-convex and (h 1 , h 2 )-convex F•I•V•Fs via fuzzy Riemannian and fuzzy Riemann-Liouville fractional integrals.…”

Section: Introductionmentioning

confidence: 99%

Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings

et al. 2022

Self Cite

View full text Add to dashboard Cite

The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractional integral inequalities are also proved via Riemann–Liouville fractional integral operator, where integrands are fuzzy-interval-valued functions. To prove the validity of our main results, some of the nontrivial examples are also provided. As specific situations, our findings can provide a variety of new and well-known outcomes which can be viewed as applications of our main results. The results in this paper can be seen as refinements and improvements to previously published findings.

show abstract

“…Moreover, Khan et al [21] exploited fuzzy order relations to introduce a new class of convex fuzzy-interval-valued functions (convex F-I•V-Fs), known as (h 1 , h 2 )-convex F-I•V-Fs, as well as a novel version of the H-H type inequality for (h 1 , h 2 )-convex F-I•V-Fs that incorporates the fuzzy interval Riemann integral. Khan et al went a step further by providing new convex and extended convex I•V-F classes, as well as new fractional H-H type and H-H type inequalities for left and right (h 1 , h 2 )-preinvex I•V-F [22], left and right p-convex I•V-Fs [23], left and right log-h-convex I•V-Fs [24], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities

et al. 2022

Self Cite

View full text Add to dashboard Cite

In this paper, we discuss the Riemann–Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex I∙V-F), as well as various related notions and concepts. First, the authors used the Riemann–Liouville fractional integral to prove Hermite–Hadamard type (𝓗–𝓗 type) inequality. Furthermore, 𝓗–𝓗 type inequalities for the product of two left and right convex I∙V-Fs have been established. Finally, for left and right convex I∙V-Fs, we found the Riemann–Liouville fractional integral Hermite–Hadamard type inequality (𝓗–𝓗 Fejér type inequality). The findings of this research show that this methodology may be applied directly and is computationally simple and precise.

show abstract

New Hermite–Hadamard-type inequalities for "Equation missing"-convex fuzzy-interval-valued functions

Cited by 70 publications

References 27 publications

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

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

Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings

Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities

Contact Info

Product

Resources

About