A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space.
A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject
A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].
In this paper, we will give a new fixed point theorem for lower semicontinuous multimaps in a Hausdorff topological vector space.
We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.
It was proved by Juhász and Weiss that for every ordinal α with there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that and α is an ordinal such that , then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all , we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic...