Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 79075, 8 pages
doi:10.1155/FPTA/2006/79075

Diametrically contractive maps and fixed points

Marco Baronti,1 Emanuele Casini,2 and Pier Luigi Papini3

1Sezione 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
2Dipartimento di Fisica e Matematica, Università dell'Insubria, Via Valleggio 11, Como 22100, Italy
3Dipartimento di Matematica, Università degli Studi di Bologna, Piazza Porta S. Donato 5, Bologna 40126, Italy

Received 13 January 2006; Revised 3 May 2006; Accepted 3 May 2006

Copyright © 2006 Marco Baronti et al. 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.

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.