7 papers
Arithmetic-geometric mean, additive, and multiplicative contractions: New generalizations of the Banach contraction principle
Irom Shashikanta Singh, Yumnam Mahendra Singh, Evgeniy Petrov +1
We introduce new contraction conditions based on classical inequality between arithmetic and geometric means. By incorporating an auxiliary semimetric , we define arithmetic-ge…
On quasisymmetric mappings between ultrametric spaces
Evgeniy Petrov, Ruslan Salimov
In 1980 P. Tukia and J. Väisälä in seminal paper [P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn., Ser. A I, Math. 5, 97--114 (1980…
On the uniqueness of continuation of a partially defined metric
Evgeniy Petrov
The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let be an undirected graph with the set of vertices and the…
On quasisymmetric mappings in semimetric spaces
Evgeniy Petrov, Ruslan Salimov
The class of quasisymmetric mappings on the real axis was first introduced by A. Beurling and L. V. Ahlfors in 1956. In 1980 P. Tukia and J. Väisälä considered these mappings be…
Weak similarities of finite ultrametric and semimetric spaces
Evgeniy Petrov
Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces and are weakly similar if there exists a weak similarity $Φ\colon X\to…
On a weighted generalization of Kendall's tau distance
Albert Bruno Piek, Evgeniy Petrov
We introduce a metric on the set of permutations of given order, which is a weighted generalization of Kendall's rank distance and study its properties. Using the edge graph o…