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Keywords = Matkowski’s theorem

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17 pages, 331 KB  
Article
Matkowski-Type Functional Contractions under Locally Transitive Binary Relations and Applications to Singular Fractional Differential Equations
by Faizan Ahmad Khan, Nidal H. E. Eljaneid, Ahmed Alamer, Esmail Alshaban, Fahad Maqbul Alamrani and Adel Alatawi
Fractal Fract. 2024, 8(1), 72; https://doi.org/10.3390/fractalfract8010072 - 22 Jan 2024
Cited by 1 | Viewed by 1856
Abstract
This article presents a few fixed-point results under Matkowski-type functional contractive mapping using locally J-transitive binary relations. Our results strengthen, enhance, and consolidate numerous existent fixed-point results. To argue for the efficacy of our results, several illustrated examples are supplied. With the [...] Read more.
This article presents a few fixed-point results under Matkowski-type functional contractive mapping using locally J-transitive binary relations. Our results strengthen, enhance, and consolidate numerous existent fixed-point results. To argue for the efficacy of our results, several illustrated examples are supplied. With the help of our findings, we deal with the existence and uniqueness theorems pertaining to the solution of a variety of singular fractional differential equations. Full article
(This article belongs to the Special Issue Nonlinear Fractional Differential Equation and Fixed-Point Theory)
11 pages, 302 KB  
Article
An Application of wt-Distances to Characterize Complete b-Metric Spaces
by Salvador Romaguera
Axioms 2023, 12(2), 121; https://doi.org/10.3390/axioms12020121 - 26 Jan 2023
Cited by 5 | Viewed by 1743
Abstract
The notion of wt-distance, introduced by Hussain et al. provides a natural generalization to the b-metric framework of the well-known and fruitful concept of w-distance, initiated by Kada et al. Since then, several authors have obtained fixed point theorems [...] Read more.
The notion of wt-distance, introduced by Hussain et al. provides a natural generalization to the b-metric framework of the well-known and fruitful concept of w-distance, initiated by Kada et al. Since then, several authors have obtained fixed point theorems for complete b-metric spaces with the help of wt-distances. In this note, we generalize the b-metric version of the celebrated Matkowski fixed point theorem, stated by Czerwik, by replacing the involved b-metric with any wt-distance on the corresponding complete b-metric space. From this result, we derive characterizations of complete b-metric spaces that constitute full generalizations of both a prominent characterization of metric completeness due to Suzuki and Takahashi, and the classical characterization of metric completeness obtained by Hu. Full article
(This article belongs to the Special Issue Advances in General Topology and Its Application)
12 pages, 276 KB  
Article
Some Fixed-Point Theorems in Proximity Spaces with Applications
by Muhammad Qasim, Hind Alamri, Ishak Altun and Nawab Hussain
Mathematics 2022, 10(10), 1724; https://doi.org/10.3390/math10101724 - 18 May 2022
Cited by 3 | Viewed by 1813
Abstract
Considering the ω-distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using ω-distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in [...] Read more.
Considering the ω-distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using ω-distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions. Full article
(This article belongs to the Special Issue New Progress in General Topology and Its Applications)
10 pages, 274 KB  
Article
A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces
by Based Ali, Mohammad Imdad and Salvatore Sessa
Axioms 2021, 10(2), 50; https://doi.org/10.3390/axioms10020050 - 2 Apr 2021
Cited by 2 | Viewed by 1922
Abstract
In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of [...] Read more.
In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of our newly proved result. Finally, as an application of our main result, we establish the existence and uniqueness of a solution of a periodic boundary value problem. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
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