Strong convergence of modified Mann iterations

By Tae-Hwa Kim, Hong-Kun Xu. 2005

281 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c6af46232cddef9e0d8a310c013ee1d0579235d9

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces ✩ (2008, unknown): “, [6,8,10,12,13,15,18,19]).”
Common zero point for a finite family of inclusion problems of accretive mappings in Banach spaces (2018, background): “[12], Kim and Xu [15], Rockafellar [9,10] and Cholamjiak [16].”
Solving variational inequalities involving nonexpansive type mappings (2008, background): “Recently, Benavides, Acedo and Xu [2], Kamimura and Takahashi [8], Kim and Xu [ 9 ], Mainge [13], Nakajo [17] and Solodov and Svaiter [21] modified proximal point algorithm to generate strongly convergent sequences.”
Strong convergence of the CQ method for fixed point iteration processes (2006, methodology): “See also [10] for another modification of the Mann iteration process (2) which also has strong convergence.”
ITERATIVE ALGORITHMS FOR NONEXPANSIVE MAPPINGS ON HADAMARD MANIFOLDS (2010, background): “Some modifications have been proposed in [20, 14] to get strong convergence.”
Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings (2007, methodology): “They improved the results of Kim and Xu [5] to some extent.”
Parallel and sequential hybrid methods for a finite family of asymptotically quasi $$\phi $$ϕ-nonexpansive mappings (2015, methodology): “For the case N = 1, Theorem 1 gives the following monotone hybrid method, which modifies the corresponding algorithms in Kim and Xu [17], as well as Kim and Takahashi (Theorems 3.”
WEAK AND STRONG CONVERGENCE THEOREMS FOR STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACES (2007, background): “Some modifications have recently been obtained (see [11,12,16,17,28]).”