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Mann-iteration process for the fixed point of strictly pseudocontractive mapping in some Banach spaces. (English) Zbl 0844.47033
Many authors constructed and examined some processes for the fixed points of strictly pseudocontractive mappings in various Banach spaces. In fact the fixed points of strictly pseudocontractive mapping are the zeroes of strongly accretive operators. So the same processes are used for both circumstances. {\it S. Reich} [Appl. Nonlin. Anal., Arlington/Texas 1978, 335-345 (1979; Zbl 0444.47042)] proved that the Mann-iteration process can be applied to approximate the zeroes of strongly accretive operators in uniformly smooth Banach spaces. In the above paper he asked whether the fact can be extended to other Banach spaces the duals of which are not necessarily uniformly convex. Recently {\it J. Schu} [Appl. Anal. 40, No. 2/3, 67-72 (1991; Zbl 0726.47040)] proved it for uniformly continuous strictly pseudocontractive mappings in smooth Banach spaces. In this paper we prove that the Mann-iteration process can be applied to approximate the fixed points of strictly pseudocontractive mappings in certain Banach spaces.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
47H07Monotone and positive operators on ordered topological linear spaces