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Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications. (English) Zbl 1215.47091
Summary: The purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, monotone hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article modify and improve the results of S.-Y. Matsushita and W. Takahashi [J. Approximation Theory 134, No. 2, 257–266 (2005; Zbl 1071.47063)], S. Plubtieng and K. Ungchittrakool [J. Approximation Theory 149, No. 2, 103–115 (2007; Zbl 1137.47056)], Y.-F. Su, Z.-M. Wang and H.-K. Xu [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, A, 5616–5628 (2009; Zbl 1206.47088)], and many others.

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties