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On the approximation of fixed points of weak contractive mappings. (English) Zbl 1114.47045
Summary: In this paper, the class of weak contractive type mappings, introduced by the author in [Nonlinear Anal. Forum 9, No. 1, 43--53 (2004; Zbl 1078.47042)] and studied in [Fixed Point Theory 4, No. 2, 131--142 (2003; Zbl 1065.47069)] is compared to some other well known contractive type mappings in Rhoades’ classification [{\it B. E. Rhoades}, Trans. Am. Math. Soc. 226, 257--290 (1977; Zbl 0365.54023)]. As corollaries of our main results, we obtain several convergence theorems for approximating fixed points by means of Picard iteration. These complete or extend the corresponding results in literature by providing error estimates, rate of convergence for the used iterative method as well as results concerning the data dependence of the fixed points.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
54H25Fixed-point and coincidence theorems in topological spaces