Search results for "metric spaces"
showing 10 items of 49 documents
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
Duality of moduli in regular toroidal metric spaces
2020
We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala [12] on the corresponding duality in condensers. peerReviewed
Solution of an initial-value problem for parabolic equations via monotone operator methods
2014
We study a general initial-value problem for parabolic equations in Banach spaces, by using a monotone operator method. We provide sufficient conditions for the existence of solution to such problem.
Some new fixed point results in non-Archimedean fuzzy metric spaces
2013
In this paper, we introduce the notions of fuzzy $(\alpha,\beta,\varphi)$-contractive mapping, fuzzy $\alpha$-$\phi$-$\psi$-contractive mapping and fuzzy $\alpha$-$\beta$-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results.
Fixed points in weak non-Archimedean fuzzy metric spaces
2011
Mihet [Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008) 739-744] proved a theorem which assures the existence of a fixed point for fuzzy $\psi$-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.
Common fixed point theorems of integral type for OWC mappings under relaxed condition
2017
In this paper, we prove a common fixed point theorem for a pair of occasionally weakly compatible (owc) self mappings satisfying a mixed contractive condition of integral type without using the triangle inequality. We prove also analogous results for two pairs of owc self mappings by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. Finally, we give an application of our results in dynamic programming.
Some common fixed point theorems for owc mappings with applications
2013
Starting from the setting of fuzzy metric spaces, we give some new common fixed point theorems for a pair of occasionally weakly compatible (owc) self-mappings satisfying a mixed contractive condition. In proving our results, we do not need to use the triangular inequality. Also we obtain analogous results for two pairs of owc self-mappings by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement some results existing in the literature. Finally, we give some applications of our results.
Nonlinear quasi-contractions of Ciric type
2012
In this paper we obtain points of coincidence and common fixed points for two self mappings satisfying a nonlinear contractive condition of Ciric type. As application, using the scalarization method of Du, we deduce a result of common fixed point in cone metric spaces.
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
2013
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
$varphi$-pairs and common fixed points in cone metric spaces
2008
In this paper we introduce a contractive condition, called $\varphi \textrm{-}pair$, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for $\varphi \textrm{-}pairs$. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.