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

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

Fumiaki Kohsaka and Wataru Takahashi

 Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
Received 12 March 2003

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.