Schu, Jürgen Approximating fixed points of Lipschitzian pseudocontractive mappings. (English) Zbl 0804.47057 Houston J. Math. 19, No. 1, 107-115 (1993). 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 \(A\). Cited in 21 Documents MSC: 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:Lipschitzian pseudocontractive selfmapping of a nonempty closed bounded and convex subset \(A\) of a Hilbert space; unique fixed point; compactness assumption PDFBibTeX XMLCite \textit{J. Schu}, Houston J. Math. 19, No. 1, 107--115 (1993; Zbl 0804.47057)