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Approximation of fixed points of strictly pseudocontractive mappings on arbitrary closed, convex sets in a Banach space. (English) Zbl 0956.47040
The authors show that any fixed point of a Lipschitzian, strictly pseudocontractive mapping $$T$$ on a closed, convex subset $$K$$ of a Banach space $$X$$ is necessarily unique, and may be norm approximated by an iterative procedure. Our argument provides a convergence rate estimate and removes the boundedness assumption on $$K$$, generalizing theorems of Liu.

MSC:
 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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References:
 [1] Liwei Liu, Approximation of fixed points of a strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1363 – 1366. · Zbl 0870.47039
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