Measures of Noncircularity and Fixed Points of Contractive Multifunctions

Measures of Noncircularity and Fixed Points of Contractive Multifunctions

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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 welding sweater 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 cyspera cream where to buy and contractive with respect to any one of these measures, has the origin as a fixed point.