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Weak and strong convergence theorems for approximating fixed points of nonexpansive mappings using a composite hybrid iteration method. (English) Zbl 1343.47068
Summary: We prove that the recent results of Y. Miao and J. Li [Appl. Anal. Discrete Math. 2, No. 2, 197–204 (2008; Zbl 1199.47279), http://pefmath.etf.bg.ac.yu] concerning the iterative approximation of fixed points of nonexpansive mappings in Hilbert spaces using a composite hybrid iteration method can be extended to arbitrary Banach spaces without the strong monotonicity assumption imposed on the hybrid operators.
##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.