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A new iterative method for common fixed points of a finite family of nonexpansive mappings. (English) Zbl 1175.54053

Let \(X\) be a real Banach space and \(C\) a nonempty closed subset of \(X\). Let \(T_i: C\to C\), \(i= 1,2,\dots, r\) be a nonexpansive mappings. For a given \(x_1\in C\), and a fixed \(r\in \mathbb N\) (\(\mathbb N\) denotes the set of all real positive integers) a new general iterative scheme is introduced.
In this paper some weak and strong convergence theorems of this iterative scheme for a finite family of nonexpansive mappings in a uniformly convex Banach space are proved which generalize the results by H. F. Senter and W. G. Dotson, jun. [Proc. Am. Math. Soc. 44, 375–380 (1974; Zbl 0299.47032)] and G. Liu, D. Lei and S. Li [Int. J. Math. Math. Sci. 24, No. 3, 173–177 (2000; Zbl 0966.47035)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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References:

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