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Some fixed point iteration procedures. (English) Zbl 0716.47030

This good survey, containing a list of 52 references, consists of three parts. In the first Section, the author passes in review some well known results about the convergence to the fixed point of an iterative process of Mann or Ishikawa type for several kinds of maps such as nonexpansive, pseudo-contractive and generalized nonexpansive maps in Banach spaces. The rate of convergence and the stability of these iteration procedures are examined in Section 2 and Section 3, respectively. Similar topics can be found in other papers of the same author [e.g., Cont. Math. 72, 233- 245 (1988; Zbl 0649.54024); J. Math. Anal. Appl. 130, 564-576 (1988; Zbl 0674.47042)].
Reviewer: S.Sessa

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
47J25 Iterative procedures involving nonlinear operators
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