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Keywords = θ-fixed circle

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24 pages, 373 KiB  
Article
Control Functions in G-Metric Spaces: Novel Methods for θ-Fixed Points and θ-Fixed Circles with an Application
by Hasanen A. Hammad, Maryam G. Alshehri and Ayman Shehata
Symmetry 2023, 15(1), 164; https://doi.org/10.3390/sym15010164 - 5 Jan 2023
Cited by 2 | Viewed by 1638
Abstract
The purpose of this paper is to present some new contraction mappings via control functions. In addition, some fixed point results for Θ,α,θ,Ψ contraction, rational Θ,α,θ,Ψ contraction and almost [...] Read more.
The purpose of this paper is to present some new contraction mappings via control functions. In addition, some fixed point results for Θ,α,θ,Ψ contraction, rational Θ,α,θ,Ψ contraction and almost Θ,α,θ,Ψ contraction mappings are obtained. Moreover, under contraction mappings of types (I), (II), and (III) of Θ,θ,Ψυ0, several fixed circle solutions are provided in the setting of a G-Metric space. Our results extend, unify, and generalize many previously published papers in this direction. In addition, some examples to show the reliability of our results are presented. Finally, a supporting application that discusses the possibility of a solution to a nonlinear integral equation is incorporated. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points)
13 pages, 760 KiB  
Article
Fixed Circle and Fixed Disc Results for New Types of Θc-Contractive Mappings in Metric Spaces
by Hayel N. Saleh, Salvatore Sessa, Waleed M. Alfaqih, Mohammad Imdad and Nabil Mlaiki
Symmetry 2020, 12(11), 1825; https://doi.org/10.3390/sym12111825 - 4 Nov 2020
Cited by 14 | Viewed by 1928
Abstract
In this manuscript, we introduce the notions of various types of Θc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we [...] Read more.
In this manuscript, we introduce the notions of various types of Θc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings, which generalize many results of invariance and transformations in the literature. Full article
(This article belongs to the Section Mathematics)
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