Abstract
Two quite useful single-valued Lipschitz continuous operators are associated with a monotone operator, namely its resolvent and its Yosida approximation. This chapter is devoted to the investigation of these operators. It exemplifies the tight interplay between firmly nonexpansive mappings and monotone operators. Indeed, firmly nonexpansive operators with full domain can be identified with maximally monotone operators via resolvents and the Minty parameterization.
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14 January 2020
The original version of this book was inadvertently published without updating the following corrections in Chapters 1, 2, 3, 6–13, 17, 18, 20, 23, 24, 26, 29, 30 and back matter. These are corrected now.
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Bauschke, H.H., Combettes, P.L. (2017). Resolvents of Monotone Operators. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_23
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DOI: https://doi.org/10.1007/978-3-319-48311-5_23
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48310-8
Online ISBN: 978-3-319-48311-5
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