| A Theorem of Iterative Approximation of Zero Point for Maximal Monotone Operator in Banach Space |
| Received:February 25, 2005 Revised:July 17, 2005 |
| Key Words:
Lyapunov functional maximal monotone operator uniformly convex Banach space Reich inequality.
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| Fund Project:the National Natural Science Foundation of China (10471003) |
| Author Name | Affiliation | | WEI Li | School of Mathematics and Statistics, Hebei University of Economics and Business, Hebei 050061, China
Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China | | ZHOU Hai-yun | Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China
Institute of Mathematics and Information Sciences, Hebei Normal University, Hebei 050016, China |
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| Abstract: |
| Let $E$ be a real smooth and uniformly convex Banach space, and $E^*$ its duality space. Let $A \subset E \times E^*$ be a maximal monotone operator with $A^{-1}0 \neq \phi$. A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator $A$ by using the techniques of Lyapunov functional, $Q_r$ operator and generalized projection operator, etc. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.01.024 |
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