Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces
Let E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/760671 |
| Summary: | Let E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a V-strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem. |
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| ISSN: | 1085-3375 1687-0409 |