Measures of Noncircularity and Fixed Points of Contractive Multifunctions

Measures of Noncircularity and Fixed Points of Contractive Multifunctions

Blog Article

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 Screen Protectors them to establish a fixed point theorem of Darbo type for multifunctions.Namely, we prove Cat Treats 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.