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Iterative approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces. (English) Zbl 0827.47041
The authors show that certain iterations introduced by S. Ishikawa [Proc. Am. Math. Soc. 44, 147-150 (1974; Zbl 0286.47036)] involving a so- called pseudo-contractive mapping T in the sense of F. Browder and W. V. Petryshyn [J. Math. Anal. Appl. 20, 197-228 (1967; Zbl 0153.457)] converges strongly to a fixed point of T. This generalizes a recent result of C. E. Chidume [Proc. Am. Math. Soc. 99, 283-288 (1987; Zbl 0646.47037)].

MSC:
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
47J05Equations involving nonlinear operators (general)