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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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[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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