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On the convergence of the Mann iteration in locally convex spaces. (English) Zbl 1174.47398
With a view to extending certain results of V. Berinde [Acta Math. Univ. Comen., New Ser. 73, No. 1, 119–126 (2004; Zbl 1100.47054)] and B. E. Rhoades [J. Math. Anal. Appl. 56, 741–750 (1976; Zbl 0353.47029)], the author obtains convergence theorems involving Mann iterations for maps in locally convex spaces.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
46A03 General theory of locally convex spaces
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