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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Published in:Abstract and Applied Analysis 2009-01, Vol.2009 (1), p.999-1018
Main Authors: Plubtieng, Somyot, Sriprad, Wanna
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Language:English
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Algorithms
Banach spaces
Mathematics
Studies
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description 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).
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subjects Algorithms
Banach spaces
Mathematics
Studies
title Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces
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