Page 1

Displaying 1 – 6 of 6

Showing per page

New fixed point theorems for mappings satisfying a generalized weakly contractive condition with weaker control functions

Hemant Kumar Nashine (2012)

Annales Polonici Mathematici

The purpose of this paper is to derive new common fixed point theorems for a pair of mappings satisfying a more general weakly contractive condition with weaker control functions in a complete metric space. Applications to new fixed point results with conditions of integral type are also given. We furnish an example to demonstrate that these results improve the previously existing ones.

Non-abelian group structure on the Urysohn universal space

Michal Doucha (2015)

Fundamenta Mathematicae

We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.

Non-locally compact Polish groups and two-sided translates of open sets

Maciej Malicki (2008)

Fundamenta Mathematicae

This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of S in terms of group actions, and prove that certain natural classes of non-locally...

Currently displaying 1 – 6 of 6

Page 1