A weak Kantorovich existence theorem for the solution of nonlinear equations

DOI10.1016/J.JMAA.2007.12.049zbMath1137.47048OpenAlexW1975172877MaRDI QIDQ2481897

Ioannis K. Argyros, Livinus Ugochukwu Uko

Publication date: 15 April 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.12.049

zbMATH Keywords

Newton's methodNewton methodmajorant methodnonlinear equationsLipschitz conditioniterative solutionmajorizing sequencecenter-Lipschitz condition

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (2)

A generalized Kantorovich theorem for nonlinear equations based on function splitting ⋮ On Newton-Kantorovich method for solving the nonlinear operator equation

Cites Work

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• On a class of nonlinear integral equations arising in neutron transport
• A new convergence theorem for the Jarratt method in Banach space
• The Kantorovich theorem and interior point methods
• Error bounds for Newton’s process derived from the Kantorovich theorem
• Quadratic equations and applications to Chandrasekhar's and related equations
• An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• On the Kantorovich Hypothesis for Newton’s Method

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