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Abstract and Applied Analysis
Volume 2004 (2004), Issue 3, Pages 239-249
http://dx.doi.org/10.1155/S1085337504309036

Strong convergence of an iterative sequence for maximal monotone operators in a Banach space

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan

Received 12 March 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.