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