Convergence of a third order method for fixed points in Banach spaces

DOI10.1007/s11075-011-9521-2zbMath1248.65057OpenAlexW2008127735MaRDI QIDQ438805

Sanjaya Kumar Parhi, Dharmendra Kumar Gupta

Publication date: 31 July 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-011-9521-2

zbMATH Keywords

convergencefixed pointnumerical examplesBanach spaceFréchet derivativenonlinear integral equationa priori error boundsnonlinear operator equations\(\omega\)-continuity conditionLipschitz and Hölder continuity conditionsStirling-like method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces, Localization and separation of solutions for Fredholm integral equations, Convergence of Traub's iteration under \(\omega\) continuity condition in Banach spaces, On the convergence of harmonic mean Newton method under \(\omega\) continuity condition in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Halley-type iterations with free second derivative
• A third order method for fixed points in Banach spaces
• Convergence of the variants of the Chebyshev-Halley iteration family under the Hölder condition of the first derivative
• Convergence of Stirling's method in Banach spaces
• Indices of convexity and concavity. Application to Halley method
• On the \(R\)-order of the Halley method
• A modification of the super-Halley method under mild differentiability conditions
• A discretization scheme for some conservative problems
• On a characterization of some Newton-like methods of \(R\)-order at least three
• Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space
• Convergence of the family of the deformed Euler--Halley iterations under the Hölder condition of the second derivative
• A Newton-like method in Banach spaces under mild differentiability conditions
• Newton's Method in Banach Spaces
• On a new multiparametric family of Newton-like methods
• Numerical Solvability of Hammerstein Integral Equations of Mixed Type
• Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
• Chebyshev's approximation algorithms and applications