New Demiclosedness Principles for (firmly) nonexpansive operators

Details New Demiclosedness Principles for (firmly) nonexpansive operators New Demiclosedness Principles for (firmly) nonexpansive operators

2011-03-04

arxiv.org/abs/1103.0991v1

Mathematics

Functional Analysis

Scientific paper

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.

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