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Keywords = Wardowski (or ℱ) contraction

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17 pages, 338 KiB  
Article
Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems
by Naeem Saleem, Bilal Iqbal, Fady Hasan and Wasfi Shatanawi
Symmetry 2023, 15(6), 1162; https://doi.org/10.3390/sym15061162 - 27 May 2023
Cited by 5 | Viewed by 1240
Abstract
The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of [...] Read more.
The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory. Full article
(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)
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