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Convex Analysis and Monotone Operator Theory in Hilbert Spaces pp 59–74Cite as

Convexity and Nonexpansiveness

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Part of the book series: CMS Books in Mathematics ((CMSBM))

Abstract

Nonexpansive operators are Lipschitz continuous operators with Lipschitz constant 1. They play a central role in applied mathematics, because many problems in nonlinear analysis reduce to finding fixed points of nonexpansive operators. In this chapter, we discuss nonexpansiveness and several variants. The properties of the fixed point sets of nonexpansive operators are investigated, in particular in terms of convexity.

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Authors and Affiliations

  1. Mathematics Irving K. Barber School, University of British Columbia, Kelowna, B.C., V1V 1V7, Canada

    Heinz H. Bauschke

  2. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris 6, 4, Place Jussieu, 75005, Paris, France

    Patrick L. Combettes

Authors
  1. Heinz H. Bauschke
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  2. Patrick L. Combettes
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Corresponding author

Correspondence to Heinz H. Bauschke .

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© 2011 Springer Science+Business Media, LLC

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Bauschke, H.H., Combettes, P.L. (2011). Convexity and Nonexpansiveness. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9467-7_4

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