An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces

: We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) 2009-06, Vol.2009 (1), p.591874-591874
Main Authors: Plubtieng, Somyot, Sriprad, Wanna
Format: Article
Language:English
Online Access:Get full text
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Summary:: We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004), and Iiduka and Takahashi (2008). Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
ISSN:1687-1812
1687-1820
1687-1812
DOI:10.1186/1687-1812-2009-591874