On the Statistical Convergence of Metric-Valued Sequences

arXiv (Cornell University), 2022

In this paper using a non-negative regular summability matrix A and a non-trivial admissible ideal I in N we study some basic properties of strong A I -statistical convergence and strong A I -statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also introduce strong A I * -statistical Cauchyness in probabilistic metric space and study its relationship with strong A I -statistical Cauchyness there. Further, we study some basic properties of strong A I -statistical limit points and strong A I -statistical cluster points of a sequence in probabilistic metric spaces.

arXiv (Cornell University), 2022

In this paper we study some basic properties of strong Astatistical convergence and strong A-statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also study some basic properties of strong A-statistical limit points and strong A-statistical cluster points of a sequence in a probabilistic metric space. Further we also introduce the notion of strong statistically A-summable sequence in a probabilistic metric space and study its relationship with strong A-statistical convergence.

THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)

In this study, using a lacunary sequence we introduce the concepts of lacunary d−statistically convergent sequences and lacunary d−statistically bounded sequences in general metric spaces.

Tatra Mountains Mathematical Publications

The aim of this paper is to study sequences of numbers as random variables. The asymptotic density will play the role of the probability. In the first part of this paper, the notion of natural metric on the set of natural numbers is defined. It is a metric so that the completion of ℕ is a compact metric space on which a probability Borel measure exists so that the sequence {n} is uniformly distributed. This condition connects the asymptotic density and the mentioned measure. A necessary and sufficient condition is derived so that a given metric is natural. Later, we study the properties of sequences uniformly continuous with respect to the given natural metric. Inter alia, the continuity ofdistribution function is characterized.

2010

In this paper, we study statistical convergence in n−normed spaces. We show that some properties of statistical convergence of real number sequences also hold for sequences in n−normed spaces. We also define the notion of a statistical Cauchy sequence in n−normed spaces. We obtain a criteria for a sequence in n−normed spaces to be a statistical Cauchy sequence. Mathematics Subject Classification: 40A05, 46A45, 46A70

Journal of Classical Analysis

Statistical convergence and statistical Cauchy sequence in 2-normed space were studied by Gürdal and Pehlivan [M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bulletin of Mathematics, (33) (2009), 257-264]. In this paper, we get analogous results of statistical convergence and statistical Cauchy sequence of functions and investigate some properties and relationships between them in 2-normed spaces.

2018

WOS: 000456892600012The main purpose of this paper is to define a new type of statistical convergence of sequences in a cone metric space and investigate the relations of these sequences with some other sequences

2014

In this paper we have introduced the concept of statistically convergent sequence in case of cone metric space and constructed statistically convergent, Cauchy and complete cone metric space and some theorems based on them. Consequently we have generalised several results in cone metric spaces from metric spaces.

International Journal of ADVANCED AND APPLIED SCIENCES

In this paper, we introduce the concepts of ∫ Γ 2 statistical convergence and strongly ∫ Γ 2 of real numbers. It is also shown that Γ 2 statistical convergence and strongly ∫ Γ 2 are equivalent for analytic sequences of real numbers. We introduce certain new double sequence spaces of ∫ Γ 2 of fuzzy real numbers defined by − convergence using sequences of Musielak-Orlicz functions and also study some basic topological and algebraic properties of these spaces, investigate the inclusion relations between these spaces.

arXiv (Cornell University), 2024

In this paper, using the concept of natural density, we have introduced the notion of rough statistical convergence which is an extension of the notion of rough convergence in a partial metric space. We have defined the set of rough statistical limit points of a sequence in a partial metric space and proved that this set is closed and bounded. Finally, we have found out the relationship between the set of statistical cluster points and the set of rough statistical limit points of sequences in a partial metric space.

2019

In this paper, the concept of deferred statistical convergence is generalized to general metric spaces, and some inclusion relations between deferred strong Ces\`{a}ro summability and deferred statistical convergence are given in general metric spaces. 

2015

In this paper we construct some generalized new difference statistically convergentsequence spaces defined by a Musielak-Orlicz function over n − normed spaces. Wealso study several properties relevant to topological structures and inclusion relationsbetween these spaces.

Abstract and Applied Analysis, 2011

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces Dini, Arzelà, and Alexandroff in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

Acta Mathematica Vietnamica, 2013

and Technology (VAST) and Springer Science +Business Media Singapore. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Proyecciones (Antofagasta), 2019