A new iterative approximation scheme for Reich–Suzuki-type nonexpansive operators with an application

In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contra...

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Published inJournal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 26
Main Authors Ofem, Austine Efut, Işık, Hüseyin, Ali, Faeem, Ahmad, Junaid
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 02.03.2022
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Approximation
Banach space
Banach spaces
Contractive-like mapping
Convergence
Fixed points (mathematics)
Game theory
Integral equations
Iterative methods
Iterative scheme
Mathematics
Mathematics and Statistics
Nonlinear integral equation
Stability
w 2 $w^{2}$ -stability
Iterative scheme
Nonlinear integral equation
47H09
Contractive-like mapping
Banach space
47H05
stability
39B82
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Abstract In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The w 2 -stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of w 2 -stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.
AbstractList In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The w2-stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of w2-stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.
Abstract In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The w 2 $w^{2}$ -stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of w 2 $w^{2}$ -stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.
In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The w 2 -stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of w 2 -stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.
In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The $w^{2}$ w 2 -stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of $w^{2}$ w 2 -stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.
ArticleNumber 28
Author Işık, Hüseyin
Ofem, Austine Efut
Ahmad, Junaid
Ali, Faeem
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  organization: Department of Engineering Science, Bandırma Onyedi Eylül University
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  organization: Department of Mathematics, Maulana Azad National Institute of Technology
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  givenname: Junaid
  surname: Ahmad
  fullname: Ahmad, Junaid
  organization: Department of Mathematics and Statistics, International Islamic University
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Keywords Iterative scheme
Nonlinear integral equation
47H09
Contractive-like mapping
Banach space
47H05
stability
39B82
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Snippet In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and...
Abstract In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and...
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SubjectTerms Analysis
Applications of Mathematics
Approximation
Banach space
Banach spaces
Contractive-like mapping
Convergence
Fixed points (mathematics)
Game theory
Integral equations
Iterative methods
Iterative scheme
Mathematics
Mathematics and Statistics
Nonlinear integral equation
Stability
w 2 $w^{2}$ -stability
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Title A new iterative approximation scheme for Reich–Suzuki-type nonexpansive operators with an application
URI https://link.springer.com/article/10.1186/s13660-022-02762-8
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Volume 2022
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