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On the convergence of the three-step iteration process in the class of quasi-contractive operators. (English) Zbl 1120.47314

Summary: We establish a general theorem to approximate fixed points of quasi-contractive operators on a normed space through the three-step iteration process. Our result generalizes and improves upon, among others, the corresponding result of V. Berinde [Acta Math. Univ. Comen., New Ser. 73, No. 1, 119–126 (2004; Zbl 1100.47054)].

MSC:

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

Citations:

Zbl 1100.47054
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