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Zbl 1126.47056
Xu, Hong-Kun
Strong convergence of approximating fixed point sequences for nonexpansive mappings.
(English)
[J] Bull. Aust. Math. Soc. 74, No. 1, 143-151 (2006). ISSN 0004-9727

The author constructs an approximating fixed point sequence $\{x_n\}$ for a mapping $T$ of a nonempty closed convex subset $C$ of a smooth and uniformly convex Banach space $X$, generated by the iteration process as the projection of an arbitrary initial point $x_0$ into the intersection of two closed convex subsets $C_n$, $Q_n$ of $C$, given by $x_{n+1}= P_{C_n\cap Q_n} x_n$. The author goes on to prove that the sequence generated is an approximating fixed point sequence for $T: C\to C$ and that it is strongly convergent to a fixed point of $T$.
[O. O. Owojori (Ife-Ife)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
65J15 Equations with nonlinear operators (numerical methods)
47H06 Accretive operators, etc. (nonlinear)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: nonexpansive self-mapping; uniform convexity; Banach contraction principle; approximating fixed point sequences

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