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Search Results (2)

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Keywords = generalized (ψ,α,β)—weak contraction

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21 pages, 357 KiB  
Article
Common Best Proximity Points and Completeness of ℱ−Metric Spaces
by Mi Zhou, Naeem Saleem, Basit Ali, Misha Mohsin and Antonio Francisco Roldán López de Hierro
Mathematics 2023, 11(2), 281; https://doi.org/10.3390/math11020281 - 5 Jan 2023
Cited by 5 | Viewed by 1948
Abstract
In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions [...] Read more.
In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F−metric spaces. Further, we obtain the best proximity point result for generalized α−φ−proximal contractions in F−metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F−metric spaces via best proximity points. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications in Nonlinear Analysis and Optimization)
14 pages, 264 KiB  
Article
Generalized (ψ,α,β)—Weak Contractions for Initial Value Problems
by Piyachat Borisut, Poom Kumam, Vishal Gupta and Naveen Mani
Mathematics 2019, 7(3), 266; https://doi.org/10.3390/math7030266 - 15 Mar 2019
Cited by 22 | Viewed by 3482
Abstract
A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation [...] Read more.
A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
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