Deferred statistical order convergence in Riesz spaces

Mathematica Slovaca, 2012

In this paper, we introduce the concepts of statistical monotone convergence and statistical order convergence in a Riesz space, and establish some basic facts. We show that the statistical order convergence and the statistical convergence in norm need not be equivalent in a normed Riesz space. Finally, we introduce the statistical order boundedness of a sequence in a Riesz space.

IOSR Journals , 2019

In this paper, the study seeks to introduce the concept of statistical order convergence and statistically relatively uniform convergence in Riesz spaces of double sequences. Which is an extension of that of recently introduced for single sequences. We shall also give the analogous definitions of statistical order convergence, statistically relatively uniform convergence and norm statistical convergence of double sequences. Finally, we shall explore and establish some inclusion relations among these concepts.

Filomat, 2019

We consider the notion of generalized density, namely, the natural density of weight 1 recently introduced in [4] and primarily study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequence under which the subsequence is also generalized statistically convergent. Also we consider similar types of results for the case of generalized statistically bounded sequence. Some results are further obtained in a more general form by using the notion of ideals. The entire investigation is performed in the setting of Riesz spaces extending the recent results in [13].

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. 

2012

Recently, the notion of statistical convergence is studied in a locally solid Riesz space by Albayrak and Pehlivan 2012 . In this paper, we define and study statistical τ-convergence, statistical τ-Cauchy and S * τ -convergence of double sequences in a locally solid Riesz space.

In this paper, deferred statistical convergence is defined by using deferred Cesàro mean instead of Cesàro mean in the definition of statistical convergence. The obtained method is compared with strong deferred Cesàro mean and statistical convergence under some certain assumptions. Also, some inclusion theorems and examples are given.

Journal of Inequalities and Applications, 2013

The concept of statistical convergence is one of the most active areas of research in the field of summability. Most of the new summability methods have relation with this popular method. In this paper, we introduce the concept of double I θ -statistical-τ -convergence which is a more general idea of statistical convergence. We also investigate the ideas of double I θ -statistical-τ -boundedness and double I θ -statistical-τ -Cauchy condition of sequences in the framework of locally solid Riesz space endowed with a topology τ and investigate some of their consequences.

2016

In this paper mainly, Wijsman deferred statistical convergence of sequence of sets in an arbitrary metric space is defined and some basic theorems are given. Besides new results, some results in this paper are the generalization of the results given in [3], [15] and [18].

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.

Filomat, 2016

In this paper, we introduce the concepts of ?m-deferred statistical convergence of order ? and strong ?mr-deferred Ces?ro summability of order ? of real sequences. Additionally, some inclusion relations about ?m-deferred statistical convergence of order ? and strong ?mr-deferred Ces?ro summability of order ? are given.