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Approximating fixed points of weak contractions using the Picard iteration. (English) Zbl 1078.47042
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.

MSC:
 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.