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Strong convergence theorems by shrinking and hybrid projection methods for relatively nonexpansive mappings in Banach spaces. (English) Zbl 1269.47050
Hsu, Sze-Bi (ed.) et al., Proceedings of the fifth international conference on nonlinear analysis and convex analysis (NACA 2007), Hsinchu, Taiwan, May 31–June 4, 2007. Yokohama: Yokohama Publishers (ISBN 978-4-946552-32-8/pbk). 7-26 (2009).
Summary: In this paper, we study iteration methods for approximating a common fixed point of a family of nonlinear mappings in a Banach space. First, we discuss some properties of relatively nonexpansive mappings and strongly relatively nonexpansive mappings. Then we obtain strong convergence theorems for a sequence of relatively nonexpansive mappings by using two hybrid projection methods. Using these results, we study the problem of finding a zero of a maximal monotone operator and a common fixed point of a countable family of relatively nonexpansive mappings.
For the entire collection see [Zbl 1225.00046].

##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H05 Monotone operators and generalizations