Strong convergence of approximation fixed points for nonexpansive nonself-mapping
Let C be a closed convex subset of a uniformly smooth Banach space E, and T:C→E a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that F(T)≠∅, and f:C→C a fixed contractive mapping. For t∈(0,1), the implicit iterative sequence {xt} is defined by xt=P(tf(xt)+(1−t)Txt), th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/16470 |
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| Summary: | Let C be a closed convex subset of a uniformly smooth Banach
space E, and T:C→E a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that F(T)≠∅, and f:C→C a fixed contractive mapping. For t∈(0,1), the implicit iterative sequence {xt} is defined by xt=P(tf(xt)+(1−t)Txt), the explicit iterative sequence {xn} is given by xn+1=P(αnf(xn)+(1−αn)Txn), where αn∈(0,1) and P is a sunny nonexpansive retraction of E onto C.
We prove that {xt} strongly converges to a fixed point of T
as t→0, and {xn} strongly converges to a fixed point of T as αn satisfying appropriate conditions. The results presented extend and improve the corresponding results of Hong-Kun Xu (2004) and Yisheng Song and Rudong Chen (2006). |
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| ISSN: | 0161-1712 1687-0425 |