The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map.

DOI10.1016/S0022-247X(03)00338-XzbMath1045.47057MaRDI QIDQ1405318

Ştefan M. Şoltuz, Billy E. Rhoades

Publication date: 25 August 2003

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

zbMATH Keywords

convergenceasymptotically nonexpansive mappingequivalence between one-step and two-step iterationsMann and Ishikawa iterations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

The equivalence between Mann-Ishikawa iterations and multistep iteration, Some results in fixed point theory and application to the convergence of some iterative processes, Simpler is also better in approximating fixed points, Improvements in stable inversion of NARX models by using Mann iteration, Hybrid approximation of solutions of integral equations of the Hammerstein type, Reconsiderations on the equivalence of convergence between Mann and Ishikawa iterations for asymptotically pseudocontractive 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, The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions, The convergence of the modified Mann and Ishikawa iterations in Banach spaces, Implication between certain iterative processes via some enriched mappings, The equivalence between the convergence of the modified Mann and Ishikawa iterations for asymptotically pseudocontractive mappings obtained by dropping the bounded assumption, Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces

Cites Work

• Iterative construction of fixed points of asymptotically nonexpansive mappings
• On the equivalence of Mann and Ishikawa iteration methods
• Nonlinear semigroups and evolution equations
• Fixed Point Iteration for Local Strictly Pseudo-Contractive Mapping
• Fixed Points by a New Iteration Method
• Mean Value Methods in Iteration