Abstract and Applied Analysis
Volume 2003 (2003), Issue 10, Pages 621-629
doi:10.1155/S1085337503207065

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

Abstract

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.