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Approximating fixed points of Lipschitzian pseudocontractive mappings. (English) Zbl 0804.47057
Summary: Let \(T\) be a Lipschitzian pseudocontractive selfmapping of a nonempty closed bounded and convex subset \(A\) of a Hilbert space \((E,(\cdot,\cdot))\) and let \(w\) be an arbitrary point of \(A\). Then the iteration procedure \(z_{n+1}:= \mu_{n+1}(a_ n T(z_ n)+ (1- a_ n)z_ n)+ (1- \mu_{n+1})w\) converges strongly to the unique fixed point of \(T\) which is closest to \(w\), provided \((\mu_ n)\) and \((a_ n)\) have certain properties. No compactness assumption is made on \(A\).

MSC:
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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