Journal of Convex Analysis 31 (2024), No. 4, 1045--1056
Copyright Heldermann Verlag 2024
Fixed Points of Generalized Pseudo-Contractions: Existence and Stability
Luc Barbet
Laboratoire de Mathématiques, Université de Pau, Pau, France
luc.barbet@univ-pau.fr
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.
Keywords: Fixed points, multivalued maps, pseudo-contractions, iterative sequences, stability, convergence.
MSC: 47H10, 47H09, 47H04.
[ Fulltext-pdf (115 KB)] for subscribers only.