Factorization theorems for extensions of maps
Fixed Point Theorems Via Various Cyclic Contractive Conditions in Partial Metric Spaces
Fixed points for cyclic orbital generalized contractions on complete metric spaces
We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some...
Fixed points of local contractions.
Fixed points of multivalued contractions with nonclosed, nonconvex values
For a class of multivalued contractions with nonclosed, nonconvex values, the set of all fixed points is proved to be nonempty and arcwise connected. Two applications are then developed. In particular, one of them is concerned with some properties of the set of all classical trajectories corresponding to continuous controls for a given nonlinear control system.
Fonctions séparément continues sur le produit de deux espaces polonais
Functor of extension of -isometric maps between central subsets of the unbounded Urysohn universal space
The aim of the paper is to prove that in the unbounded Urysohn universal space there is a functor of extension of -isometric maps (i.e. dilations) between central subsets of to -isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group acts continuously on by -isometries.