Fixed Points of Order Preserving Multifunctions

Fixed Points of Order Preserving Multifunctions

Let F:X-*X be a multifunction on a partially ordered set (X, ¿). Suppose for each pair «iá*2 and for each yi<EF(xi) there is a yi&F{y¿) such that yièyiThen sufficient conditions are given such that multifunctions F satisfying the above condition will have a fixed point. These results generalize the Tarski Theorem on complete lattices, and they also generalize some results of S. Abian and A. B. ...

Measures of Noncircularity and Fixed Points of Contractive Multifunctions

In analogy to the Eisenfeld-Lakshmikanthammeasure of nonconvexity and theHausdorffmeasure 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 a...

On fixed points of quasi-contraction type multifunctions

In 2009, Ilić and Rakoc̆ević proved that quasi-contraction maps on normal cone metric spaces have a unique fixed point (Ilić and Rakoc̆ević, 2009 [6]). Then, Kadelburg, Radenović and Rakoc̆ević generalized their results by considering an additional assumption (Kadelburg et al., 2009 [7]). Also, they proved that quasi-contraction maps on cone metric spaces have the property (P) whenever λ ∈ (0, 2 )...

Measure Preserving Homeomorphisms at Fixed Points

In an article of a few years ago [2] Kerékjartó obtained interesting results about certain types of transformations which he called similitudes. With a few modifications and extensions his methods can be used to gain information about the structure of measure preserving transformations at fixed points. For simplicity the results are formulated for Euclidean w-space although they could easily be...

Two Results about Fixed Point of Multifunctions