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Strong convergence of monotone hybrid algorithm for hemi-relatively nonexpansive mappings. (English) Zbl 1203.47078
Summary: The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi [J. Approximation Theory 134, No. 2, 257–266 (2005; Zbl 1071.47063)] can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi [op. cit.] and some others.

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
[5] · doi:10.1090/S0273-0979-1992-00287-2