Search results for "metric space"

Information and hierarchical structure in financial markets

1999

I investigate the information content present in the time series of stock prices of a portfolio of stocks traded in a financial market. By investigating the correlation coefficient between pairs of stocks I provide a working definition of a generalized distance between the stocks of the portfolio. This generalized distance is used to obtain an ultrametric distance matrix between the stocks. The ultrametric structure of the portfolio investigated has associated a taxonomy which is meaningful from an economic point of view.

From fuzzy metric spaces to modular metric spaces: a fixed point approach

2017

We propose an intuitive theorem which uses some concepts of auxiliary functions for establishing existence and uniqueness of the fixed point of a self-mapping. First we work in the setting of fuzzy metric spaces in the sense of George and Veeramani, then we deduce some consequences in modular metric spaces. Finally, a sample homotopy result is derived making use of the main theorem.

Thin and fat sets for doubling measures in metric spaces

2011

We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.

Approximate fixed points of set-valued mapping in b-metric space

2016

We establish existence results related to approximate fixed point property of special types of set-valued contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some fixed point results which generalize and extend various fixed point theorems in the existing literature. A simple example illustrates the new theory. Finally, we apply our results to establishing the existence of solution for some differential and integral problems.

Common Fixed points for multivalued generalized contractions on partial metric spaces

2013

We establish some common fixed point results for multivalued mappings satisfying generalized contractive conditions on a complete partial metric space. The presented theorems extend some known results to partial metric spaces. We motivate our results by some given examples and an application for finding the solution of a functional equation arising in dynamic programming.

Basic Sequences in the Dual of a Fréchet Space

2001

Some fixed point theorems for generalized contractive mappings in complete metric spaces

2015

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.

Set-Valued Generalizations of Baire′s Category Theorem

1995

Abstract We prove some generalizations of Baire′s category theorem for chains of iterates of multifunctions defined on Cech-complete spaces. In particular, we extend Lennard′s results stated for functions on complete metric spaces.

A note on best approximation in 0-complete partial metric spaces

2014

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

Common Fixed Points in a Partially Ordered Partial Metric Space

2013

In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.