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Displaying 241 –
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Let (X, d) be a metric space and CL(X) the family of all
nonempty closed subsets of X. We provide a new proof of the fact that the
coincidence of the Vietoris and Wijsman topologies induced by the metric
d forces X to be a compact space. In the literature only a more involved
and indirect proof using the proximal topology is known. Here we do not
need this intermediate step. Moreover we prove that (X, d) is boundedly
compact if and only if the bounded Vietoris and Wijsman topologies on
CL(X) coincide....
In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.
Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.
In this paper we extend the concept of -weak commutativity to the setting of single-valued and multivalued mappings. We also establish a coincidence theorem for pairs of -weakly commuting single-valued and multivalued mappings satisfying a contractive type condition.
Currently displaying 241 –
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