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Search Results (4)

Search Parameters:
Keywords = (φ,θ)-contraction

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12 pages, 294 KiB  
Article
Relation-Theoretic Fixed Point Theorems Involving Certain Auxiliary Functions with Applications
by Nifeen Hussain Altaweel and Faizan Ahmad Khan
Symmetry 2022, 14(12), 2614; https://doi.org/10.3390/sym14122614 - 9 Dec 2022
Cited by 6 | Viewed by 1502
Abstract
This article includes some fixed point results for (φ,ψ,θ)-contractions in the context of metric space endowed with a locally H-transitive relation. We constructed an example for attesting to the credibility of our results. We also [...] Read more.
This article includes some fixed point results for (φ,ψ,θ)-contractions in the context of metric space endowed with a locally H-transitive relation. We constructed an example for attesting to the credibility of our results. We also discussed the existence and uniqueness of the solution of a Fredholm integral equation using our results. Full article
(This article belongs to the Section Mathematics)
23 pages, 338 KiB  
Article
Fixed Point Theorems on Almost (φ,θ)-Contractions in Jleli-Samet Generalized Metric Spaces
by Doru Dumitrescu and Ariana Pitea
Mathematics 2022, 10(22), 4239; https://doi.org/10.3390/math10224239 - 13 Nov 2022
Cited by 5 | Viewed by 1595
Abstract
In this paper, we present extensions of some classic results regarding the existence and uniqueness of fixed points of operators fulfilling generalized contractive conditions defined by sums involving some functions with suitable properties in the setting of Jleli–Samet generalized metric spaces. As a [...] Read more.
In this paper, we present extensions of some classic results regarding the existence and uniqueness of fixed points of operators fulfilling generalized contractive conditions defined by sums involving some functions with suitable properties in the setting of Jleli–Samet generalized metric spaces. As a consequence, some known results in the literature are obtained. Examples are provided to prove the usability of our developments. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
9 pages, 1210 KiB  
Article
The Symmetry of the Interior and Exterior of Schwarzschild and Reissner–Nordstrom Black Holes—Sphere vs. Cylinder
by Andy T. Augousti, Andrzej Radosz, Pawel Gusin and Aleksander Kaczmarek
Symmetry 2020, 12(5), 859; https://doi.org/10.3390/sym12050859 - 23 May 2020
Cited by 1 | Viewed by 3242
Abstract
One can question the relationship between the symmetries of the exterior and interior of black holes with an isotropic and static exterior. This question is justified by the variety of recent findings indicating substantial or even dramatic differences in the properties of the [...] Read more.
One can question the relationship between the symmetries of the exterior and interior of black holes with an isotropic and static exterior. This question is justified by the variety of recent findings indicating substantial or even dramatic differences in the properties of the exterior and interior of isotropic, static black holes. By invoking some of these findings related to a variety of the thought experiments with freely falling or uniformly accelerated test particles, one can establish the dynamic properties of the interior, which turn out to be equivalent to anisotropic cosmology, simultaneously expanding and contracting, albeit in different directions. In order to illustrate the comparison between the symmetry of the exterior vs. the interior, we apply conventional t, r, θ, φ coordinates to both of these ranges, although on the horizon(s) they display singular behavior. Using a simple approach based on co-moving and freely falling observers, the dynamics of the cylindrically shaped interior are explored. That enables us to present schematic snapshots of the interior of a Schwarzschild black hole, expanding along its cylindrical axis and contracting along its spherical base, as well as the interior of a Reissner–Nordström black hole, expanding first and then contracting along the cylindrical axis up to the terminal instant r =r−. Full article
(This article belongs to the Special Issue Selected Papers: Symmetry 2019—The Second Edition of the International Conference on Symmetry)
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14 pages, 255 KiB  
Article
Best Proximity Results on Dualistic Partial Metric Spaces
by Ariana Pitea
Symmetry 2019, 11(3), 306; https://doi.org/10.3390/sym11030306 - 1 Mar 2019
Cited by 14 | Viewed by 1997
Abstract
We introduce the generalized almost ( φ , θ ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost θ -Geraghty contractions in the setting [...] Read more.
We introduce the generalized almost ( φ , θ ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost θ -Geraghty contractions in the setting of dualistic partial metric spaces are defined by the use of a function of Geraghty type and another adequate auxiliary function. For these classes of generalized contractions, we have stated and proved the existence and uniqueness of a best proximity point. Full article
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