A fixed point theorem in o-minimal structures

A fixed point theorem in o-minimal structures

Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps. Résumé Dans cet article nous montrons un théorème de point fixe o-minimal pour les applications définissables continues sur les ensembles définissables et définissablement compacts, qui générali...

Whitney’s Extension Theorem in O-minimal Structures

In 1934, Whitney gave a necessary and sufficient condition on a jet of order m on a closed subset E of R to be the jet of order m of a C-function; jets satisfying this condition are known as C-Whitney fields. Later, Paw lucki and Kurdyka proved that subanalytic C-Whitney fields are jets of order m of sybanalytic C-functions. Here, we work in an o-minimal expansion of a real closed field and pro...

A 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].

A Fixed Point Theorem in Generalized D-metric Spaces

Vector ultrametric spaces and a fixed point theorem for correspondences

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.