Abstract
The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this note, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many (firmly) nonexpansive operators are presented. As an application, a simple proof of the weak convergence of the Douglas-Rachford splitting algorithm is provided. © Springer Science+Business Media New York 2013.
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Bauschke, H. H. (2013). New Demiclosedness Principles for (Firmly) Nonexpansive Operators. In Springer Proceedings in Mathematics and Statistics (Vol. 50, pp. 19–28). Springer New York LLC. https://doi.org/10.1007/978-1-4614-7621-4_2
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