On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space

Alqudah, Manar A.; Kashuri, Artion; Mohammed, Pshtiwan Othman; Raees, Muhammad; Abdeljawad, Thabet; Anwar, Matloob; Hamed, Y. S.

doi:10.3934/math.2021273

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Sana¹,

Khan²,

Noor³

et al. 2021

IJCIS

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It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function. The single-valued function and interval-valued function both are special cases of fuzzy interval-valued function. The aim of this paper is to introduce a new class of convex fuzzy interval-valued functions, which is called harmonically convex fuzzy interval-valued functions (harmonically convex fuzzy-IVFs) by means of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann-Liouville fractional operator. With the help of fuzzy order relation and fuzzyinterval Riemann-Liouville fractional, we derive some integrals inequalities of Hermite-Hadamard (H-H) type and Hermite-Hadamard-Fejér (H-H Fejér) type as well as some product inequities for harmonically convex fuzzy-IVFs. Our results represent a significant improvement and refinement of the known results. We hope that these interesting outcomes may open a new direction for fuzzy optimization, modeling and interval-valued function.

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Section: Introductionmentioning

confidence: 99%

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

Sana¹,

Khan²,

Noor³

et al. 2021

IJCIS

Self Cite

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Fractional Weighted Ostrowski-Type Inequalities and Their Applications

et al. 2021

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An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.

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New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation

Khan¹,

Mohammed²,

Noor³

et al. 2021

MATH

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<abstract> <p>It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, the inclusion relation (⊆) and fuzzy order relation $\left(\preccurlyeq \right)$ both are two different concepts, respectively. In this article, with the help of fuzzy order relation, we introduce fractional Hermite-Hadamard inequality (<italic>HH</italic>-inequality) for <italic>h</italic>-convex fuzzy-interval-valued functions (<italic>h</italic>-convex-IVFs). Moreover, we also establish a strong relationship between <italic>h</italic>-convex fuzzy-IVFs and Hermite-Hadamard Fejér inequality (<italic>HH</italic>-Fejér inequality) via fuzzy Riemann Liouville fractional integral operator. It is also shown that our results include a wide class of new and known inequalities for <italic>h</italic>-convex fuzz-IVFs and their variant forms as special cases. Nontrivial examples are presented to illustrate the validity of the concept suggested in this review. This paper's techniques and approaches may serve as a springboard for further research in this field.</p> </abstract>

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On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space

Cited by 4 publications

References 39 publications

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

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

Fractional Weighted Ostrowski-Type Inequalities and Their Applications

New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation

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