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Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications. (English) Zbl 1201.65091
Summary: Some properties of the generalized $f$-projection operator are proved in Banach spaces. Using these results, the strong convergence theorems for relatively nonexpansive mappings are studied in Banach spaces. As applications, the strong convergence of general $H$-monotone mappings in Banach spaces is also given. The results presented in this paper generalize and improve the main results of {\it S. Matsushita} and {\it W. Takahashi} [J. Approximation Theory 134, No. 2, 257--266 (2005; Zbl 1071.47063)].

MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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References:
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