Convergence Theorems for a Maximal Monotone Operator and a 𝑉-Strongly Nonexpansive Mapping in a Banach Space
Let E be a smooth Banach space with a norm ‖⋅‖. Let 𝑉(𝑥,𝑦)=‖𝑥‖2+‖𝑦‖2−2⟨𝑥,𝐽𝑦⟩ for any 𝑥,𝑦∈𝐸, where ⟨⋅,⋅⟩ stands for the duality pair and J is the normalized duality mapping. With respect to this bifunction 𝑉(⋅,⋅), a generalized nonexpansive mapping and a 𝑉-strongly nonexpansive mapping are defined in...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/189814 |
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| Summary: | Let E be a smooth Banach space with a norm ‖⋅‖. Let 𝑉(𝑥,𝑦)=‖𝑥‖2+‖𝑦‖2−2⟨𝑥,𝐽𝑦⟩ for any 𝑥,𝑦∈𝐸, where ⟨⋅,⋅⟩ stands for the duality
pair and J is the normalized duality mapping. With respect to this bifunction
𝑉(⋅,⋅), a generalized nonexpansive mapping and a 𝑉-strongly nonexpansive
mapping are defined in 𝐸. In this paper, using the properties of generalized
nonexpansive mappings, we prove convergence theorems for common zero
points of a maximal monotone operator and a 𝑉-strongly nonexpansive mapping. |
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| ISSN: | 1085-3375 1687-0409 |