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Zbl 1064.47068
Kohsaka, Fumiaki; Takahashi, Wataru
Strong convergence of an iterative sequence for maximal monotone operators in a Banach space.
(English)
[J] Abstr. Appl. Anal. 2004, No. 3, 239-249 (2004). ISSN 1085-3375; ISSN 1687-0409/e

Authors' abstract: We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by {\it S. Kamimura} and {\it W. Takahashi} in a Hilbert space [J. Approximation Theory 106, No. 2, 226--240 (2000; Zbl 0992.47022)]. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.''
[Zhang Xian (Xiamen)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H05 Monotone operators (with respect to duality)

Keywords: maximal monotone operators; strong convergence

Citations: Zbl 0992.47022

Cited in: Zbl 1211.90285

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