Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods
Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our...
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| Published in | Journal of applied mathematics Vol. 2020; no. 2020; pp. 1 - 12 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1110-757X 1687-0042 |
| DOI | 10.1155/2020/5198520 |
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| Abstract | Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ-strictly pseudocontractive mappings, solution of α-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type. |
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| AbstractList | Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ-strictly pseudocontractive mappings, solution of α-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type. Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of [lambda]-strictly pseudocontractive mappings, solution of [alpha]-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type. Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ -strictly pseudocontractive mappings, solution of α -inverse-strongly monotone mappings, and solution of integral equations of Fredholm type. |
| Audience | Academic |
| Author | Thakur, Surendra Aibinu, Mathew O. Moyo, Sibusiso |
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| Copyright | Copyright © 2020 Mathew Aibinu et al. COPYRIGHT 2020 John Wiley & Sons, Inc. Copyright © 2020 Mathew Aibinu et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Banach spaces Inequality Integral equations Iterative algorithms Iterative methods Mapping Mathematical analysis Nonlinear equations Operators (mathematics) Viscosity |
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| Title | Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods |
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