Mann iteration of weak convergence theorems in Banach space
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Publication:844051
DOI10.1007/s10255-007-7054-1zbMath1178.47045OpenAlexW1982563083MaRDI QIDQ844051
Publication date: 18 January 2010
Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10255-007-7054-1
weak convergencefixed pointMann iteration\(k\)-strictly pseudocontractive mappings\(p\)-uniformly convex
Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)
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Iterative process for a strictly pseudo-contractive mapping in uniformly convex Banach spaces ⋮ Strong convergence of iterative algorithms with variable coefficients for generalized equilibrium problems, variational inequality problems and fixed point problems ⋮ Strong convergence theorems for strict pseudocontractions in uniformly convex Banach spaces ⋮ Strong convergence theorems of viscosity iterative methods for a countable family of strict pseudo-contractions in Banach spaces ⋮ Boundary Point Method and Mann-Dotson’s Algorithm for Nonself Strict Pseudo-contractive Mappings in Uniformly Smooth Banach Spaces ⋮ Theorems of strong convergence of mixed iterative methods for obtaining strict pseudocontractions in Banach spaces ⋮ The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces
Cites Work
- Iterative construction of fixed points of asymptotically nonexpansive mappings
- Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
- On Mann iteration in Hilbert spaces
- Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively \(\Phi \)-pseudocontractive mappings without Lipschitzian assumptions
- An implicit iteration process with errors for a finite family of \(r\)-strictly asymptotically pseudocontractive mappings
- A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
- Weak convergence theorems for nonexpansive mappings in Banach spaces
- Strongly unique best approximations and centers in uniformly convex spaces
- Convergence theorems for sequences of nonlinear operators in Banach spaces
- Construction of fixed points of nonlinear mappings in Hilbert space
- An example on the Mann iteration method for Lipschitz pseudocontractions
- Iterative Approximation of Fixed Points of Lipschitzian Strictly Pseudo-Contractive Mappings
- Inequalities in Banach spaces with applications
- Weak convergence of the sequence of successive approximations for nonexpansive mappings
- Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings
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