Abstract

We present an extension of Nadler's fixed point theorem and its local version for a class of multivalued maps that contains the pseudo-contractions. Relatively to a modulus, we propose conditions to ensure existence of fixed points with a quantitative estimate (depending on the modulus) about the distance of a reference point to the fixed point set. Some stability properties are established and are applied to the study of convergence of fixed point sets.

Author information

Contact details are reproduced from the original publication and may be historical.

Luc Barbet

Laboratoire de Mathématiques, Université de Pau, Pau, France
and: CNRS UMR 5142, Pau, France

luc.barbet@univ-pau.fr

Keywords

  • Fixed points
  • multivalued maps
  • pseudo-contractions
  • iterative sequences
  • stability
  • convergence

Mathematics Subject Classification

47H10, 47H09, 47H04

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Suggested citation

L. Barbet. “Fixed Points of Generalized Pseudo-Contractions: Existence and Stability.” Journal of Convex Analysis 31 (2024), No. 4, 1045–1056. https://doi.org/10.68381/jca31053

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.