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Keywords = extended Branciari b-metric spaces

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25 pages, 486 KB  
Article
Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations
by Reena Jain, Hemant Kumar Nashine and Reny George
Fractal Fract. 2024, 8(1), 20; https://doi.org/10.3390/fractalfract8010020 - 26 Dec 2023
Cited by 2 | Viewed by 2247
Abstract
We introduce the concept of controlled extended Branciari quasi-b-metric spaces, as well as a Gq-implicit type mapping. Under this new space setting, we derive some new fixed points, periodic points, right and left Ulam–Hyers stability, right and left weak [...] Read more.
We introduce the concept of controlled extended Branciari quasi-b-metric spaces, as well as a Gq-implicit type mapping. Under this new space setting, we derive some new fixed points, periodic points, right and left Ulam–Hyers stability, right and left weak well-posed properties, and right and left weak limit shadowing results. Additionally, we use these findings to solve the fractional differential equations of a Riesz–Caputo type with integral anti-periodic boundary values, as well of nonlinear matrix equations. All ideas, results, and applications are properly illustrated with examples. Full article
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8 pages, 278 KB  
Article
Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space
by Pragati Gautam, Luis Manuel Sánchez Ruiz and Swapnil Verma
Symmetry 2021, 13(1), 32; https://doi.org/10.3390/sym13010032 - 28 Dec 2020
Cited by 20 | Viewed by 3738
Abstract
The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the [...] Read more.
The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result. Full article
(This article belongs to the Special Issue Advanced Calculus in Problems with Symmetry)
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