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.


47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.