On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application

In this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of thes...

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Main Authors: Fayyaz Ahmad, Kifayat Ullah, Junaid Ahmad, Om Kalthum S. K. Mohamed, Awad A. Bakery
Format: Article
Language:English
Published: Wiley 2023-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2023/5459916
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author Fayyaz Ahmad
Kifayat Ullah
Junaid Ahmad
Om Kalthum S. K. Mohamed
Awad A. Bakery
author_facet Fayyaz Ahmad
Kifayat Ullah
Junaid Ahmad
Om Kalthum S. K. Mohamed
Awad A. Bakery
author_sort Fayyaz Ahmad
collection DOAJ
description In this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of these mappings in a Banach space setting. We provided both weak and strong convergence results under some mild conditions on the mapping, domain, and on the parameters involved in our iterative scheme. To support these results numerically, we constructed a new example of GABN mappings and proved that the JA iterative scheme converges to its fixed point. Moreover, we proved that JA iterative scheme converges faster to the fixed point corresponding to the some other iterative schemes of the literature. Eventually, we carried out an application of our main outcome to solve a split feasibility of problems (SFPs) in the setting of GABN mappings. Thus, our results were new in the literature and improved well-known results of the literature.
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publishDate 2023-01-01
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series Journal of Mathematics
spelling doaj-art-c3298596aac04fafbf497f9e293c1c832025-08-20T02:18:54ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/5459916On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive ApplicationFayyaz Ahmad0Kifayat Ullah1Junaid Ahmad2Om Kalthum S. K. Mohamed3Awad A. Bakery4Department of Mathematical SciencesDepartment of Mathematical SciencesDepartment of MathematicsUniversity of JeddahUniversity of JeddahIn this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of these mappings in a Banach space setting. We provided both weak and strong convergence results under some mild conditions on the mapping, domain, and on the parameters involved in our iterative scheme. To support these results numerically, we constructed a new example of GABN mappings and proved that the JA iterative scheme converges to its fixed point. Moreover, we proved that JA iterative scheme converges faster to the fixed point corresponding to the some other iterative schemes of the literature. Eventually, we carried out an application of our main outcome to solve a split feasibility of problems (SFPs) in the setting of GABN mappings. Thus, our results were new in the literature and improved well-known results of the literature.http://dx.doi.org/10.1155/2023/5459916
spellingShingle Fayyaz Ahmad
Kifayat Ullah
Junaid Ahmad
Om Kalthum S. K. Mohamed
Awad A. Bakery
On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
Journal of Mathematics
title On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
title_full On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
title_fullStr On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
title_full_unstemmed On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
title_short On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
title_sort on fixed point convergence results for a general class of nonlinear mappings with a supportive application
url http://dx.doi.org/10.1155/2023/5459916
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