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Strong convergence theorems of one-step iterative scheme for a countable family of multivalued mappings in a Banach space

Bunyawat A., Suantai S.

Fasciculi Mathematici

2014

Nr 53

31--38

In this paper, we introduce a new one-step iterative scheme for finding a common fixed point of a countable family of multivalued mappings in a real uniformly convex Banach space. By using the best approximation operators, a necessary and sufficient condition for strong convergence of the proposed method is given. Moreover, we establish some strong convergence theorems of the proposed iterative scheme under some control conditions