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Convergence theorems of a general composite iterative method for nonexpansive semigroups in Banach spaces. (English) Zbl 1215.65113

Summary: We introduce a general composite iterative scheme for nonexpansive semigroups in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under different control conditions. The results presented in this paper improve and extend the corresponding results of G. Marino and H. K. Xu [J. Math. Anal. Appl. 318, No. 1, 43–52 (2006; Zbl 1095.47038)], and others, from Hilbert spaces to Banach spaces.

MSC:

65K05 Numerical mathematical programming methods
47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems

Citations:

Zbl 1095.47038
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