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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 {\it 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 {\it F. Browder} and {\it 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 {\it C. E. Chidume} [Proc. Am. Math. Soc. 99, 283-288 (1987; Zbl 0646.47037)].

##### MSC:
 47H09 Mappings defined by “shrinking” properties 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces 47J25 Iterative procedures (nonlinear operator equations) 47J05 Equations involving nonlinear operators (general)
##### Keywords:
iterations; pseudo-contractive mapping; fixed point
Full Text:
##### References:
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