A Selection Theorem in Metric Trees
نویسندگان
چکیده
In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set valued mapping T ∗ of a metric tree M with convex values has a selection T : M → M for which d(T (x), T (y)) ≤ dH(T ∗(x), T ∗(y)) for each x, y ∈ M . Here by dH we mean the Hausdroff distance. Many applications of this result are given.
منابع مشابه
Generalized multivalued $F$-contractions on non-complete metric spaces
In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...
متن کاملFIXED POINT THEOREM OF KANNAN-TYPE MAPPINGS IN GENERALIZED FUZZY METRIC SPACES
Binayak et al in [1] proved a fixed point of generalized Kannan type-mappings in generalized Menger spaces. In this paper we extend gen- eralized Kannan-type mappings in generalized fuzzy metric spaces. Then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. Finally we present an example of our main result.
متن کاملFIXED POINT TYPE THEOREM IN S-METRIC SPACES
A variant of fixed point theorem is proved in the setting of S-metric spaces
متن کاملA unique common fixed point theorem for six maps in g-metric spaces
In this paper we obtain a unique common xed point theorem for sixweakly compatible mappings in G-metric spaces.
متن کاملA RELATED FIXED POINT THEOREM IN n FUZZY METRIC SPACES
We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].
متن کامل