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Diametrically contractive maps and fixed points

Fixed Point Theory and Applications volume 2006, Article number: 79075 (2006) Cite this article

Abstract

Contractive maps have nice properties concerning fixed points; a big amount of literature has been devoted to fixed points of nonexpansive maps. The class of shrinking (or strictly contractive) maps is slightly less popular: few specific results on them (not applicable to all nonexpansive maps) appear in the literature and some interesting problems remain open. As an attempt to fill this gap, a condition half way between shrinking and contractive maps has been studied recently. Here we continue the study of the latter notion, solving some open problems concerning these maps.

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Authors and Affiliations

  1. Sezione Metodi e Modelli Matematici Dipartimento di Ingegneria della Produzione, Termoenergetica e Metodi e Modelli Matematici, Università degli Studi di Genova, Piazzale Kennedy, Genova, 16129, Italy

    Marco Baronti

  2. Dipartimento di Fisica e Matematica, Università dell'Insubria, Via Valleggio 11, Como, 22100, Italy

    Emanuele Casini

  3. Dipartimento di Matematica, Università degli Studi di Bologna, Piazza Porta S. Donato 5, Bologna, 40126, Italy

    Pier Luigi Papini

Authors
  1. Marco Baronti
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  2. Emanuele Casini
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  3. Pier Luigi Papini
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Correspondence to Marco Baronti.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Baronti, M., Casini, E. & Papini, P.L. Diametrically contractive maps and fixed points. Fixed Point Theory Appl 2006, 79075 (2006). https://doi.org/10.1155/FPTA/2006/79075

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