Viscosity approximative methods to Cesàro means for non-expansive mappings

DOI10.1016/j.amc.2006.08.054zbMath1121.65063OpenAlexW1985911574MaRDI QIDQ884558

Yisheng Song, Ru Dong Chen

Publication date: 6 June 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.054

zbMATH Keywords

convergenceiterationvariational inequalitynonexpansive mappingBanach spaceCesàro meannonlinear ergodic theoryviscosity approximate method

Mathematics Subject Classification ID

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

Related Items

Strong convergence theorems of Cesàro-type means for nonexpansive mapping in CAT(0) space ⋮ Ergodic approximations via matrix regularization approach ⋮ Viscosity approximation methods with weak contraction for L-Lipschitzian pseudocontractive self-mapping ⋮ On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings ⋮ Viscosity approximation to common fixed points of families of nonexpansive mappings with weakly contractive mappings ⋮ Iterative convergence to Cesàro means for continuous pseudocontractive mappings ⋮ Strong convergence on iterative methods of Cesàro means for nonexpansive mapping in Banach space ⋮ Viscosity approximative methods to Cesàro mean iterations for nonexpansive nonself-mappings in Banach spaces ⋮ Strong convergence of Cesàro mean iterations for nonexpansive nonself-mappings in Banach spaces ⋮ Strong convergence of averaged iteration for asymptotically non-expansive mappings ⋮ Equivalent theorems of the convergence between proximal type algorithms ⋮ Convergence analysis of generalized viscosity implicit rules for a nonexpansive semigroup with gauge functions ⋮ Convergence comparison of several iteration algorithms for the common fixed point problems ⋮ Mann iteration of Cesàro means for asymptotically non-expansive mappings

Cites Work

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• Strong convergence of averaging iterations of nonexpansive nonself-mappings
• Strong convergence theorems on two iterative method for non-expansive mappings
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces
• An iterative approach to quadratic optimization
• Viscosity approximation methods for nonexpansive mappings
• Some geometric properties related to the fixed point theory for nonexpansive mappings
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Fixed points of nonexpanding maps

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