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Zbl 1078.47042
Berinde, Vasile
Approximating fixed points of weak contractions using the Picard iteration. (English)
[J] Nonlinear Anal. Forum 9, No. 1, 43-53 (2004). ISSN 1226-7228

The results of the present paper extend Banach's, Zamfirescu's and many others' related results and further offer methods for approximating fixed points for which both a priori and a posteriori estimates are available. In particular, remarks 3, 4 of the paper are worth to note. Finally, the paper opens up frontiers of research with two important open problems in the forms of Problem 1 and Problem 2.
[Edward Prempeh (Kumasi)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties

Keywords: metric spaces; contractive maps; weak contraction fixed points; convergence theorems; error estimates

Cited in: Zbl 1224.54096 Zbl 1210.47078 Zbl 1199.54205 Zbl 1149.54025 Zbl 1114.47045

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