Search results for "metric space"
showing 10 items of 316 documents
Finitely randomized dyadic systems and BMO on metric measure spaces
2015
Abstract We study the connection between BMO and dyadic BMO in metric measure spaces using finitely randomized dyadic systems, and give a Garnett–Jones type proof for a theorem of Uchiyama on a construction of certain BMO functions. We obtain a relation between the BMO norm of a suitable expectation over dyadic systems and the dyadic BMO norms of the original functions in different systems. The expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions. Applying our result, we derive Uchiyama’s theorem from its dyadic counterpart, which we also prove.
Injective spaces of real-valued functions with the baire property
1995
Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.
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.
Fixed point results for nonexpansive mappings on metric spaces
2015
In this paper we obtain some fixed point results for a class of nonexpansive single-valued mappings and a class of nonexpansive multi-valued mappings in the setting of a metric space. The contraction mappings in Banach sense belong to the class of nonexpansive single-valued mappings considered herein. These results are generalizations of the analogous ones in Khojasteh et al. [Abstr. Appl. Anal. 2014 (2014), Article ID 325840].
The fractal interpolation for countable systems of data
2003
In this paper we will extend the fractal interpolation from the finite case to the case of countable sets of data. The main result is that, given an countable system of data in [a, b] ? Y, where [a, b] is a real interval and Y a compact and arcwise connected metric space, there exists a countable iterated function system whose attractor is the graph of a fractal interpolation function.
Fixed point results on metric and partial metric spaces via simulation functions
2015
We prove existence and uniqueness of fixed point, by using a simulation function and a lower semi-continuous function in the setting of metric space. As consequences of this study, we deduce several related fixed point results, in metric and partial metric spaces. An example is given to support the new theory.
On fixed points for a–n–f-contractive multi-valued mappings in partial metric spaces
2015
Recently, Samet et al. introduced the notion of α-ψ-contractive type mappings and established some fixed point theorems in complete metric spaces. Successively, Asl et al. introduced the notion of αӿ-ψ-contractive multi-valued mappings and gave a fixed point result for these multivalued mappings. In this paper, we establish results of fixed point for αӿ-admissible mixed multivalued mappings with respect to a function η and common fixed point for a pair (S; T) of mixed multi-valued mappings, that is, αӿ-admissible with respect to a function η in partial metric spaces. An example is given to illustrate our result.
Common fixed point theorems for multi-valued maps
2012
Abstract We establish some results on coincidence and common fixed points for a two-pair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.
Meir-Keeler Type Contractions for Tripled Fixed Points
2012
Abstract In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.
Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results
2014
Abstract We give some fixed point theorems in the setting of metric spaces or partial metric spaces endowed with a finite number of graphs. The presented results extend and improve several well-known results in the literature. In particular, we discuss a Caristi type fixed point theorem in the setting of partial metric spaces, which has a close relation to Ekelandʼs principle.