Search results for "Pseudometric space"
showing 9 items of 9 documents
Fuzzy $$\varphi $$ -pseudometrics and Fuzzy $$\varphi $$ -pseudometric Spaces
2017
By replacing the axiom \(m(x,x,t) = 1\) for all \(x\in X, t>0\) in the definition of a fuzzy pseudometric in the sense of George-Veeramani with a weaker axiom \(m(x,x,t) = \varphi (t)\) for all \(x\in X, t>0\) where \(\varphi : {\mathbb R}^+ \rightarrow (0,1]\) is a non-decreasing function, we come to the concept of a fuzzy \(\varphi \)-pseudometric space. Basic properties of fuzzy \(\varphi \)-pseudometric spaces and their mappings are studied. We show also an application of fuzzy \(\varphi \)-pseudometrics in the words combinatorics.
On a theorem of Khan in a generalized metric space
2013
Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given.
Quasi-pseudometric properties of the Nikodym-Saks space
2003
[EN] For a non-negative finite countably additive measure μ defined on the σ-field Σ of subsets of Ω, it is well known that a certain quotient of Σ can be turned into a complete metric space Σ (Ω), known as the Nikodym-Saks space, which yields such important results in Measure Theory and Functional Analysis as Vitali-Hahn-Saks and Nikodym's theorems. Here we study some topological properties of Σ (Ω) regarded as a quasi-pseudometric space.
Existence of a common fixed point for a family of mappings of non‐expansive type on a metric space
1992
Existence of a common fixed point for a family of mappings of non‐expansive type on a metric space with a closure operator is proved.
Transformations by diagonal matrices in a normed space
1962
Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space
2009
Abstract A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.
Henstock type integral in compact zero-dimensional metric space and quasi-measures representations
2012
Properties of a Henstock type integral defined on a compact zero-dimensional metric space are studied. Theorems on integral representation of so-called quasi-measures, i.e., linear functionals on the space of “polynomials” defined on the space of the above mentioned type, are obtained.
Graphical metric space: a generalized setting in fixed point theory
2016
Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with the space. Some consequences, examples and an application to integral equations are presented to confirm the significance and unifying power of obtained generalizations.
Fixed point results on metric-type spaces
2014
Abstract In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.