Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 340631, 12 pages
Research Article

Measures of Noncircularity and Fixed Points of Contractive Multifunctions

Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain

Received 24 October 2010; Accepted 8 December 2010

Academic Editor: N. J. Huang

Copyright © 2010 Isabel Marrero. 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.


In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.