Measures of Noncircularity and Fixed Points of Contractive Multifunctions
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Fixed Point Theory and Applications 2010, 2010:340631 doi:10.1155/2010/340631Published: 14 December 2010
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.