Set-Valued and Variational Analysis

, Volume 20, Issue 1, pp 131–153

Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality

  • Heinz H. Bauschke
  • Sarah M. Moffat
  • Xianfu Wang
Article

DOI: 10.1007/s11228-011-0187-7

Cite this article as:
Bauschke, H.H., Moffat, S.M. & Wang, X. Set-Valued Anal (2012) 20: 131. doi:10.1007/s11228-011-0187-7

Abstract

The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximally monotone operators due to Minty. In this paper, we systematically analyze the relationship between properties of firmly nonexpansive mappings and associated maximally monotone operators. Dual and self-dual properties are also identified. The results are illustrated through several examples.

Keywords

Banach contractionConvex functionFirmly nonexpansive mappingFixed pointHilbert spaceLegendre functionMaximally monotone operatorNonexpansive mappingParamonotoneProximal mapRectangularResolventSubdifferential operator

Mathematics Subject Classifications (2010)

Primary 47H0547H09; Secondary 26B2552A4190C25

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Heinz H. Bauschke
    • 1
  • Sarah M. Moffat
    • 1
  • Xianfu Wang
    • 1
  1. 1.Department of Mathematics, Irving K. Barber SchoolUBC OkanaganKelownaCanada