The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence

The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence

Charles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iter...

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Main Authors: Linxin Li, Dingping Wu
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9064369
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spelling doaj-ff8def1b097b407a8f10661f3c2d48212021-08-02T00:00:29ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/9064369The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of ConvergenceLinxin Li0Dingping Wu1Department of MathematicsDepartment of MathematicsCharles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ−hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.http://dx.doi.org/10.1155/2021/9064369
collection DOAJ
language English
format Article
sources DOAJ
author Linxin Li
Dingping Wu
spellingShingle Linxin Li
Dingping Wu
The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
Journal of Mathematics
author_facet Linxin Li
Dingping Wu
author_sort Linxin Li
title The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
title_short The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
title_full The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
title_fullStr The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
title_full_unstemmed The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
title_sort convergence of three-step iterative schemes for generalized φ−hemi-contractive mappings and the comparison of their rate of convergence
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description Charles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ−hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.
url http://dx.doi.org/10.1155/2021/9064369
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AT dingpingwu theconvergenceofthreestepiterativeschemesforgeneralizedphhemicontractivemappingsandthecomparisonoftheirrateofconvergence
AT linxinli convergenceofthreestepiterativeschemesforgeneralizedphhemicontractivemappingsandthecomparisonoftheirrateofconvergence
AT dingpingwu convergenceofthreestepiterativeschemesforgeneralizedphhemicontractivemappingsandthecomparisonoftheirrateofconvergence
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