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
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.
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