Open Access

Diametrically contractive maps and fixed points

Fixed Point Theory and Applications20062006:79075

https://doi.org/10.1155/FPTA/2006/79075

Received: 13 January 2006

Accepted: 3 May 2006

Published: 18 September 2006

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’ Affiliations

(1)
Sezione Metodi e Modelli Matematici Dipartimento di Ingegneria della Produzione, Termoenergetica e Metodi e Modelli Matematici, Università degli Studi di Genova
(2)
Dipartimento di Fisica e Matematica, Università dell'Insubria
(3)
Dipartimento di Matematica, Università degli Studi di Bologna

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Copyright

© Marco Baronti et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.