Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces

DOI10.1186/1687-1812-2012-78zbMath1273.49033OpenAlexW2137248365WikidataQ59289648 ScholiaQ59289648MaRDI QIDQ372097

Krishna Kumar Singh, Vipin Kumar Singh, Daya Ram Sahu

Publication date: 11 October 2013

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2012-78

zbMATH Keywords

Newton's methodfixed-pointFréchet derivativenonlinear operator equationsquasi-contraction\(S\)-operatorBanach contraction theorem

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (5)

On the convergence of Newton-like MS method with dynamics and applications ⋮ The local and semilocal convergence analysis of new Newton-like iteration methods ⋮ Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ Higher order methods of the basic family of iterations via \(S\)-iteration scheme with \(s\)-convexity

Cites Work

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• On a class of Newton-like methods for solving nonlinear equations
• On convergence of the modified Newton's method under Hölder continuous Fréchet derivative
• Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems
• Computational theory of iterative methods.
• Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space
• Newton's Method in Banach Spaces
• Convergence and Applications of Newton-type Iterations
• Fixed Point Theory for Lipschitzian-type Mappings with Applications
• A Unified Convergence Theory for a Class of Iterative Processes
• On the Kantorovich Hypothesis for Newton’s Method

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