Implicit iteration process of nonexpansive non-self-mappings
Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u+αnT[(1−βn)xn+βnTxn], yn=(1−αn)u+αnPT[(...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3103 |
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| Summary: | Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u+αnT[(1−βn)xn+βnTxn], yn=(1−αn)u+αnPT[(1−βn)yn+βnPTyn], and zn=P[(1−αn)u+αnTP[(1−βn)zn+βnTzn]], where {αn}⊆(0,1), 0≤βn≤β<1 and αn→1 as n→∞. Our results extend and improve the recent ones announced by Xu and Yin, and many others. |
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| ISSN: | 0161-1712 1687-0425 |