Principle of Weakly Contractive Maps in Hilbert Spaces

  • Ya. I. Alber
  • S. Guerre-Delabriere
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)


We introduce a class of contractive maps on closed convex sets of Hilbert spaces, called weakly contractive maps, which contains the class of strongly contractive maps and which is contained in the class of nonexpansive maps. We prove the existence of fixed points for the weakly contractive maps which are a priori degenerate in general case. We establish then the convergence in norm of classical iterative sequences to fixed points of these maps, give estimates of the convergence rate and prove the stability of the convergence with respect to some perturbations of these maps. Our results extend Banach principle previously known for strongly contractive map only.


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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Ya. I. Alber
    • 1
  • S. Guerre-Delabriere
    • 2
  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael
  2. 2.University Paris VIParisFrance

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