On convergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings
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 \textit{M. K. Ghosh} and \textit{L. Debnath} [J. Math. Anal. Appl. 207, 96-103 (1997; Zbl 0881.47036)], \textit{W. A. Kirk} [Ann. Univ. Mariae Curie-Skłodowska, Sect. A 51, 167-178 (1997; Zbl 1012.47035)] and \textit{W. V. Petryshyn} and \textit{T. E. Williamson jun.} [J. Math. Anal. Appl. 43, 459-497 (1973; Zbl 0262.47038)]. Some examples are presented.
scientific article; zbMATH DE number 1866637