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Zbl 0734.47036
Schu, Jürgen
Iterative construction of fixed points of asymptotically nonexpansive mappings. (English)
[J] J. Math. Anal. Appl. 158, No.2, 407-413 (1991). ISSN 0022-247X

Let T be a completely continuous and asymptotically non-expansive self- mapping (in the sense of Goebel and Kirk) of a nonempty closed bounded and convex subset of a Hilbert space. The author gives conditions under which a fixed point of T may be obtained as limit of the Mann-type iterates $x\sb{n+1}=\alpha\sb nT\sp n(x\sb n)+(1-\alpha\sb n)x\sb n.$ A parallel result is obtained for a new class of operators (called ``asymptotically pseudocontractive'') whose iterates admit a universal Lipschitz constant.
[J.Appell (Würzburg)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties

Keywords: completely continuous and asymptotically non-expansive self-mapping; nonempty closed bounded and convex subset of a Hilbert space; fixed point; Mann-type iterates; asymptotically pseudocontractive; universal Lipschitz constant

Cited in: Zbl 1205.65186 Zbl 1163.47308 Zbl 1176.47057 Zbl 1138.47052 Zbl 1117.47055 Zbl 1148.47049 Zbl 1104.65053 Zbl 1057.47073 Zbl 1020.47064 Zbl 0989.47044 Zbl 0968.47017 Zbl 0982.47039 Zbl 0971.47038 Zbl 0807.47045

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