Browsing by Author "Furqan, Salman"

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Citation - WoS: 7
Citation - Scopus: 7
Extended Rectangular Fuzzy B-Metric Space With Application
(Amer inst Mathematical Sciences-aims, 2022) Furqan, Salman; Abbas, Mujahid; Jarad, Fahd; Saleem, Naeem
In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a ' Ciric type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy b-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation.
Citation - WoS: 7
Citation - Scopus: 7
On Extended B-Rectangular and Controlled Rectangular Fuzzy Metric-Like Spaces With Application
(Wiley, 2022) Furqan, Salman; Jarad, Fahd; Saleem, Naeem
In this article, we introduce the notions of extended b-rectangular and controlled rectangular fuzzy metric-like spaces that generalize many fuzzy metric spaces in the literature. We give examples to justify our newly defined fuzzy metric-like spaces and prove that these spaces are not Hausdorff. We use fuzzy contraction and prove Banach fixed point theorems in these spaces. As an application, we utilize our main results to solve the uniqueness of the solution of a differential equation occurring in the dynamic market equilibrium.