arXiv subjects

Evgeniy Petrov

Publications and source records attributed to Evgeniy Petrov.

23 records · Page 2Linked to original sources

arXiv2024

Periodic points of mappings contracting total pairwise distance

We consider a new type of mappings in metric spaces so-called mappings contracting total pairwise distance on $n$ points. It is shown that such mappings are continuous. A theorem on the existence of periodic points for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary as well as the fixed-point theorem for mappings contracting perimeters of triangles. Examples of mappings contracting total pairwise distance on $n$ points and having different properties are constructed.

math.GN↗

arXiv2023

Fixed point theorem for generalized Kannan type mappings

We introduce a new type of mappings in metric spaces which are three-point analogue of the well-known Kannan type mappings and call them generalized Kannan type mappings. It is shown that in general case such mappings are discontinuous but continuous at fixed points as well as Kannan type mappings and that these two classes of mappings are independent. The fixed-point theorem for generalized Kannan type mappings is proved. Additional conditions of asymptotic regularity and continuity allow us to extent the class of mappings for which the fixed-point theorems hold. Following Kannan, we also obtain two other fixed-point theorems for generalized Kannan type mappings in metric spaces which are not obligatory complete.

math.GN↗

arXiv2023

Fixed point theorem for mappings contracting perimeters of triangles

We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary. An example of a mapping contractive perimeters of triangles which is not a contraction mapping is constructed.

math.GN↗

arXiv2019

On equicontinuous families of mappings in metric spaces

The article is devoted to the study of mappings with finite distortion in metric spaces. Analogues of results relating to equicontinuity and normality of families of quasiregular mappings are obtained. It is proved that the indicated families are equicontinuous if the characteristic of the mappings has a finite mean oscillation at each inner point, and the maps omit a certain fixed continuum. An equicontinuity of generalized quasiisometries on Riemannian manifolds is also obtained.

math.CV↗

arXiv2012

Weak similarities of metric and semimetric spaces

Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strictly increasing f : D(Y) \to D(X) such that dX = f \circ dY \circ F. It is shown that the weak similarities between geodesic spaces are usual similarities and every weak similarity F : X \to Y is an isometry if X and Y are ultrametric and compact with D(X) = D(Y). Some conditions under which the weak similarities are homeomorphisms or uniform equivalences are also found.

math.MG↗