Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators

DOI10.1016/S0898-1221(03)90183-0zbMath1067.47079OpenAlexW1985514919MaRDI QIDQ1879551

Yanyan Li

Publication date: 23 September 2004

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

Full work available at URL: https://doi.org/10.1016/s0898-1221(03)90183-0

zbMATH Keywords

Ishikawa iterationuniformly smooth Banach space\(\phi\)-strongly accretive operatormultivalued operators

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Set-valued operators (47H04) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

On the equivalence of the convergence criteria between modified Mann-Ishikawa and multi-step iterations with errors for successively strongly pseudo-contractive operators ⋮ A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings ⋮ Convergence theorems for fixed points of uniformly continuous \(\phi\)-pseudo-contractive-type operator ⋮ Iterative algorithms with variable coefficients for multivalued generalized \(\Phi \)-hemicontractive mappings without generalized Lipschitz assumption ⋮ The equivalence of convergence results between Ishikawa and Mann iterations with errors for uniformly continuous generalized \(\Phi\)-pseudocontractive mappings in normed linear spaces ⋮ Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators ⋮ A new iteration process for finite families of generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings ⋮ Convergence theorems for fixed points of uniformly continuous generalized \(\varPhi\)-hemi-contractive mappings ⋮ 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

Cites Work

• Iterative process with errors to locally strictly pseudocontractive maps in Banach spaces
• Ishikawa and Mann iterative processes with error for nonlinear strongly accretive operator equations
• Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces
• On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
• Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces
• 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
• Nonlinear semigroups and evolution equations
• Global iteration schemes for strongly pseudo-contractive maps
• Fixed point iteration for pseudocontractive maps
• Approximation of Fixed Points of Strongly Pseudocontractive Mappings
• Fixed Points by a New Iteration Method
• Steepest descent approximations for accretive operator equations
• Nonlinear mappings of nonexpansive and accretive type in Banach spaces
• Mean Value Methods in Iteration

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