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Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces. (English) Zbl 1218.47131
Let $C$ be a nonempty closed convex subset of a real Banach space $X$ whose norm is uniformly Gâteaux differentiable and let $T : C\to C$ be a continuous pseudocontraction with nonempty fixed point set $F(T)$. A sequence $(x_n)$ is defined iteratively which converges strongly to a fixed point of $T$. For all the continuous pseudocontractive mappings for which it is possible to construct the sequence $(x_n)$, the obtained result improves and extends a recent result of {\it Y.-H. Yao}, {\it Y.-C. Liou} and {\it R.-D. Chen} [Nonlinear Anal., Theory Methods Appl. 67, No. 12, A, 3311--3317 (2007; Zbl 1129.47059)].

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H05Monotone operators (with respect to duality) and generalizations
Full Text: DOI
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