Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces

DOI10.1016/S0898-1221(98)00112-6zbMath0938.47042MaRDI QIDQ1806446

Zhen Yu Huang

Publication date: 25 June 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

uniformly smooth Banach spaceIshikawa iterative sequencecontinuous \(\Phi\)-hemicontractive operator

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Convergence theorems for finite families of \(\Phi \)-strongly pseudocontractive mappings ⋮ Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators ⋮ On the equivalence of the convergence criteria between modified Mann-Ishikawa and multi-step iterations with errors for successively strongly pseudo-contractive operators ⋮ The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption ⋮ Modified Noor iterations for nonlinear equations in Banach spaces ⋮ Convergence of steepest descent approximation for set-valued quasi-accretive mapping equations ⋮ Iterative process to \(\varphi\)-hemicontractive operator and \(\varphi\)-strongly accretive operator equations ⋮ Approximations for fixed points of \(\phi\)-hemicontractive mappings by the Ishikawa iterative process with mixed errors ⋮ Perturbed iterative process for fixed points of multivalued \(\phi\)-hemicontractive mappings in Banach spaces ⋮ Weak stability of the Ishikawa iteration procedures for \(\phi\)-hemicontractions and accretive operators ⋮ Three-step iterations with errors for nonlinear strongly accretive operator equations ⋮ Weak stability of Mann and Ishikawa iterations with errors for \(\phi\)-hemicontractive operators ⋮ Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively \(\Phi \)-pseudocontractive mappings without Lipschitzian assumptions ⋮ Iterative process with errors for fixed points of multivalued \(\Phi\)-hemicontractive operators in uniformly smooth Banach spaces ⋮ Convergence of iterative processes with errors for set-valued pseudocontractive and accretive type mappings in Banach spaces ⋮ Three-step iterations for nonlinear accretive operator equations

Cites Work

• Unnamed Item
• Iterative process with errors to locally strictly pseudocontractive maps in Banach spaces
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Iterative solution of nonlinear equations with strongly accretive operators
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
• An iterative procedure for constructing zeros of accretive sets in Banach spaces
• Steepest descent approximations for accretive operator equations

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