Fixed points for contractive multifunctions

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...

Fixed Points for w-Contractive Multimaps

Fixed Points for Contractive Type Multimaps

Without using the concept of the Hausdorff metric, we prove some results on the existence of fixed points and strict fixed points for multivalued maps satisfying some generalized Latif-Albar type conditions. Consequently, several known fixed point results either generalized or improved including the corresponding recent results of Feng and Liu [J. Math. Anal. Appl. 317 (2006) 103-112], Latif an...

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. ...

Fixed and common fixed points for $(psi,varphi)$-weakly contractive mappings in $b$-metric spaces

In this paper, we give a fixed point theorem for $(psi,varphi)$-weakly contractive mappings in complete $b$-metric spaces. We also give a common fixed point theorem for such mappings in complete $b$-metric spaces via altering functions. The given results generalize two known results in the setting of metric spaces. Two examples are given to verify the given results.