The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations

DOI10.1016/S0895-7177(03)00113-4zbMath1065.47054MaRDI QIDQ597557

Yeol Je Cho, Shi Sheng Zhang, Jong Kyu Kim

Publication date: 6 August 2004

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

zbMATH Keywords

non-expansive mappinguniformly \(L\)-Lipschitzian mappingasymptotically non-expansive mapping

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Simpler is also better in approximating fixed points ⋮ An Example of Data Dependence Result for The Class of Almost Contraction Mappings ⋮ The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous \(\varphi \)-strongly accretive operators in uniformly smooth Banach spaces ⋮ Numerical and theoretical analysis for fixed points for solving differential equation with retarded argument using an efficient iterative method ⋮ The new modified Ishikawa iteration method for the approximate solution of different types of differential equations ⋮ A reconsideration on equivalency of convergence between iterations for uniformly \(L\)-Lipschitzian operators

Cites Work

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• The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings
• Fixed point iterations for real functions
• On the Mann iteration process in a Hilbert space
• Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces
• The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings
• An example on the Mann iteration method for Lipschitz pseudocontractions
• Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings
• Fixed Points by a New Iteration Method
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Mean Value Methods in Iteration

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