Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory
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چکیده
Utilizing our recent proximal-average based results on the constructive extension of monotone operators, we provide a novel approach to the celebrated Kirszbraun-Valentine Theorem and to the extension of firmly nonexpansive mappings.
منابع مشابه
General Resolvents for Monotone Operators: Characterization and Extension
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood and analyzed from the alternative viewpoint of firmly nonexpansive mappings, which were found to be precisely the resolvents of monotone operators. For examp...
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تاریخ انتشار 2008