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Strong Convergence Theorems for Nonexpansive Mappings and Nonexpansive Semigroups

open access: yesJournal of Mathematical Analysis and Applications, 2003
Let \(C\) be a nonempty closed convex subset of a real Hilbert space and \(T:C\to C\) be a nonexpansive mapping. In the present paper, the authors investigate the sequence \(\{x_n\}\) generated by: \[ \begin{cases} x_0=x\in C,\\ y_n=\alpha_nx_n+ (1-\alpha_n)Tx_n,\;\alpha_n \in [0,a),\;a\in[0,1),\\ C_n=\bigl\{z\in C:\| y_n-z\|\leq\| x_n-z \| \bigr ...
Wataru Takahashi
exaly   +2 more sources

Iterated Nonexpansive Mappings [PDF]

open access: yesJournal of Fixed Point Theory and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Enrique Llorens-Fuster   +2 more
exaly   +4 more sources
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Fixed points of nonexpansive and quasi-nonexpansive mappings

The Journal of Analysis, 2018
As answers to open questions raised by \textit{V. Colao} and \textit{G. Marino} [Fixed Point Theory Appl. 2015, Paper No. 39, 7 p. (2015; Zbl 1307.47077)], the authors show strong and weak convergence of the iterated sequence by the Krasnoselskii-Mann algorithm for a countable family of (quasi-)nonexpansive non-self mappings satisfying a weakly inward ...
Narayanan, M. Sankara, Marudai, M.
openaire   +1 more source

Nonexpansive and locally nonexpansive mappings in product spaces

Nonlinear Analysis: Theory, Methods & Applications, 1988
Let E and F be Banach spaces with \(X\subset E\) and \(Y\subset F\).
Kirk, W. A., Martinez Yanez, Carlos
openaire   +2 more sources

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