On Fuzzy b-Metric-Like Spaces

Javed, Khalil; Uddin, Fahim; Aydi, Hassen; Arshad, Muhammad; Ishtiaq, Umar; Alsamir, Habes

doi:10.1155/2021/6615976

Cited by 21 publications

(14 citation statements)

References 21 publications

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“…They also defined the fractional derivative of Riemann-Liouville. See the references [15][16][17] for the most recent paper on fuzzy differential equations.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Iqbal

Niazi

Shafqat

et al. 2021

Journal of Function Spaces

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In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0 c D I γ x I = α x I + P I , x I + A I W I , I ∈ 0 , T , x I 0 = x 0 , in which γ ∈ 0 , 1 , E 1 is the fuzzy metric space and I = 0 , T is a real line interval. With the help of few conditions on functions P : I × E 1 × E 1 ⟶ E 1 , W I is control and it belongs to E 1 , A ∈ F I , L E 1 , and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.

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“…They also defined the fractional derivative of Riemann-Liouville. See the references [15][16][17] for the most recent paper on fuzzy differential equations.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Iqbal

Niazi

Shafqat

et al. 2021

Journal of Function Spaces

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“…Javed et al [14] presented the idea of fuzzy b-metric-like spaces (FBMLSs) and proved several fixed point results. Mehmood et al [15] presented the concept of fuzzy rectangular b-metric spaces (FRBMSs) and proved the Banach contraction principle in the sense of FRBMS.…”

Section: Introductionmentioning

confidence: 99%

Some New Aspects in the Intuitionistic Fuzzy and Neutrosophic Fixed Point Theory

Hussain

Alsulami

Ishtiaq

2022

Journal of Function Spaces

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In this manuscript, we use the concepts of continuous t-norms and continuous t-conorms to introduce some definitions, in which intuitionistic fuzzy rectangular metric spaces, intuitionistic fuzzy rectangular metric-like spaces, intuitionistic fuzzy rectangular b-metric spaces, intuitionistic fuzzy rectangular b-metric-like spaces, neutrosophic rectangular metric spaces, neutrosophic rectangular metric-like spaces, neutrosophic rectangular b-metric spaces, and neutrosophic rectangular b-metric-like spaces are included. Continuous t-norms and continuous t-conorms are used to generalize the probability distribution of triangular inequalities in metric space axioms. Nontrivial examples, some fixed point results, and an application to the integral equation are imparted in this manuscript.

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“…Afterward, the utility of FMS appeared in applied sciences such as fixed point theory, image and signal processing, medical imaging, and decision-making. is classical result was generalized in different spaces, and different structures were attained using this topic, and one may recall the existing notions, ordered theoretic results in fuzzy b metric spaces [4], fuzzy b-metric-like spaces [5], orthogonal control fuzzy metric spaces [6], fuzzy generalized prioritized weighted average operator [7], fuzzy C-means clustering with locality preservation [8], the measure of divergence with fuzzy [9], and many more.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results in Orthogonal Neutrosophic Metric Spaces

et al. 2021

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Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metric space. Some fixed point results are investigated in this setting. For the validity of the obtained results, some nontrivial examples are given.

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On Fuzzy b-Metric-Like Spaces

Cited by 21 publications

References 21 publications

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Some New Aspects in the Intuitionistic Fuzzy and Neutrosophic Fixed Point Theory

Fixed Point Results in Orthogonal Neutrosophic Metric Spaces

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