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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Bibliographic Details
Published inJournal of applied mathematics Vol. 2020; no. 2020; pp. 1 - 12
Main Authors Aibinu, Mathew O., Moyo, Sibusiso, Thakur, Surendra
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Wiley
Subjects
Banach spaces
Inequality
Integral equations
Iterative algorithms
Iterative methods
Mapping
Mathematical analysis
Nonlinear equations
Operators (mathematics)
Viscosity
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ISSN1110-757X
1687-0042
DOI10.1155/2020/5198520

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Summary: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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ISSN:1110-757X
1687-0042
DOI:10.1155/2020/5198520