Let H be a real Hilbert space. Suppose that T is a nonexpansive mapping on H with a fixed point, f is a contraction on H with coefficient 0 < Ξ± < 1, and 2 )/Ξ± = Ο /Ξ±. We proved that the sequence {x n } generated by the iterative method )Tx n converges strongly to a fixed point x β F ix (T ), which
A general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces
β Scribed by Cuijie Zhang, Songnian He
- Book ID
- 120735716
- Publisher
- Springer International Publishing AG
- Year
- 2013
- Tongue
- English
- Weight
- 222 KB
- Volume
- 2013
- Category
- Article
- ISSN
- 1687-1820
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π SIMILAR VOLUMES
Let H be a real Hilbert space. Consider the iterative sequence where Ξ³ > 0 is some constant, f : H β H is a given contractive mapping, A is a strongly positive bounded linear operator on H and W n is the W -mapping generated by an infinite countable family of nonexpansive mappings T 1 , T 2 , . . .
In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding res