Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces

We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and i...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2009-01, Vol.2009 (1), p.999-1018
Main Authors: Plubtieng, Somyot, Sriprad, Wanna
Format: Article
Language:English
Subjects:
Algorithms
Banach spaces
Mathematics
Studies
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Summary:We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005).
ISSN:1085-3375
1687-0409
DOI:10.1155/2009/795432