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Zbl 0979.47038
Chidume, C.E.
Iterative approximation of fixed points of Lipschitz pseudocontractive maps. (English)
[J] Proc. Am. Math. Soc. 129, No.8, 2245-2251 (2001). ISSN 0002-9939; ISSN 1088-6826/e

Let $E$ be a $q$-uniformly smooth Banach space with a weakly sequentially continuous duality map and $T$ be a Lipschitzian pseudocontractive selfmapping of a nonempty closed bounded and assume $\chi$ be in $K$. The author's gives an iterative approximation method for a fixed point of $T$. If $E$ is a Hilbert space the approximation converges to the fixed point closest to $\chi$.
[Marco Biroli (Monza)]

MSC 2000:: *47H09 Mappings defined by "shrinking" properties
47J05 Equations involving nonlinear operators (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J25 Methods for solving nonlinear operator equations (general)

Keywords: pseudocontractive operators; $q$-uniformly smooth spaces; duality maps; weak sequential continuity.; iterative approximation; fixed point

Cited in: Zbl 1054.47056

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