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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 S. Matsushita and W. Takahashi [J. Approximation Theory 134, No. 2, 257–266 (2005; Zbl 1071.47063)].

##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems
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##### References:
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