Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications

In this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Mo...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 7; p. 1400
Main Authors Hammad, Hasanen A., Kattan, Doha A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2023
Subjects
Algorithms
Approximation
Banach spaces
Convergence
Game theory
Iterative methods
Mapping
Stability analysis
Technology application
Volterra integral equations
Germany
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ISSN2073-8994
2073-8994
DOI10.3390/sym15071400

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Summary:In this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Moreover, some numerical experiments were investigated to illustrate the behavior and efficacy of our iterative scheme. The proposed method converges faster than symmetrical iterations of the S algorithm, Thakur algorithm and K* algorithm. Eventually, as an application, the nonlinear Volterra integral equation with delay was solved using the suggested method.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym15071400