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Keywords = strong b-metric space (SbMS)

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12 pages, 258 KiB  
Article
On a Version of Dontchev and Hager’s Inverse Mapping Theorem
by Thanaa A. Alarfaj and Saud M. Alsulami
Axioms 2024, 13(7), 445; https://doi.org/10.3390/axioms13070445 - 30 Jun 2024
Viewed by 1092
Abstract
By revisiting an open question raised by Kirk and Shahzad, we are able to prove a generalized version of Nadler’s fixed-point theorem in the context of strong b-metric space. Such a result leads us to prove a new version of Dontchev and [...] Read more.
By revisiting an open question raised by Kirk and Shahzad, we are able to prove a generalized version of Nadler’s fixed-point theorem in the context of strong b-metric space. Such a result leads us to prove a new version of Dontchev and Hager’s inverse mapping theorem. Some examples are provided to illustrate the results. Full article
(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
12 pages, 277 KiB  
Article
New Generalization of Metric-Type Spaces—Strong Controlled
by Dania Santina, Wan Ainun Mior Othman, Kok Bin Wong and Nabil Mlaiki
Symmetry 2023, 15(2), 416; https://doi.org/10.3390/sym15020416 - 4 Feb 2023
Cited by 7 | Viewed by 1988
Abstract
In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: [...] Read more.
In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: (s,r)(s,z)+η(z,r)(z,r), and keeping the symmetry condition that is (s,r)=(r,s)forallr,s. We demonstrate the existence of the fixed point of self-mapping and its uniqueness in such spaces that satisfy linear and nonlinear contractions. Moreover, we provide three applications of results to polynomial equations of high degree, systems of linear equations, along with fractional differential equations. Full article
(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)
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