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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/189814 |