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.  
Fund Project:the National Natural Science Foundation of China (10471003)
Author NameAffiliation
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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