Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 574907 | https://doi.org/10.1155/S1085337503207065

Takanori Ibaraki, Yasunori Kimura, Wataru Takahashi, "Convergence theorems for generalized projections and maximal monotone operators in Banach spaces", Abstract and Applied Analysis, vol. 2003, Article ID 574907, 9 pages, 2003. https://doi.org/10.1155/S1085337503207065

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

Received20 Jan 2002

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.

Copyright © 2003 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.


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