Abstract and Applied Analysis
Volume 2003 (2003), Issue 10, Pages 621-629

Convergence theorems for generalized projections and maximal monotone operators in Banach spaces

Takanori Ibaraki,1,2 Yasunori Kimura,1,2 and Wataru Takahashi1

1Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
2Institute of Economic Research, Hitotsubashi University, Tokyo 186-8603, Japan

Received 20 January 2002

Copyright © 2003 Takanori Ibaraki et al. 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 study a sequence of generalized projections in a reflexive, smooth, and strictly convex Banach space. Our result shows that Mosco convergence of their ranges implies their pointwise convergence to the generalized projection onto the limit set. Moreover, using this result, we obtain strong and weak convergence of resolvents for a sequence of maximal monotone operators.