Abstract and Applied Analysis
Volume 2004 (2004), Issue 3, Pages 239-249
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 Fumiaki Kohsaka and Wataru Takahashi. 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.
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.