On convergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings. (English) Zbl 1024.47036
Assuming that a selfmap of a metric space is quasi-nonexpansive with respect to a sequence of points, the author presents some conditions which guarantee the convergence of some sequences to a fixed point of the mapping. The results obtained generalize some results of M. K. Ghosh and L. Debnath [J. Math. Anal. Appl. 207, 96-103 (1997; Zbl 0881.47036)], W. A. Kirk [Ann. Univ. Mariae Curie-Skłodowska, Sect. A 51, 167-178 (1997; Zbl 1012.47035)] and W. V. Petryshyn and T. E. Williamson jun. [J. Math. Anal. Appl. 43, 459-497 (1973; Zbl 0262.47038)]. Some examples are presented.
Reviewer: Janusz Matkowski (Zielona Gora)
References:
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