Concept Of Statistical Convergence Research Articles

Statistical limit superior and limit inferior in intuitionistic fuzzy normed spaces

Abstract Recently, the concepts of statistical convergence, ideal convergence and lacunary statistical convergence have been studied in intuitionistic fuzzy normed spaces. In this article, we study the concepts of statistical limit superior and statistical limit inferior in intuitionistic fuzzy normed spaces. We also give an example to compute these points in intuitionistic fuzzy normed spaces. AMS Subject Classification (2000): 40A05; 40D25; 11B05; 60H10; 60B99; 26A03.

On Λ-statistical convergence in random 2-normed space

Recently, Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of � -statistical convergence and � -statistical Cauchy sequences in random 2-normed spaces , where λ = (λm) be a non-decreasing sequence of positive numbers tending to infinity such that λm+1 ≤ λm + 1, λ1 = 1 and prove some theorems. In last section we will give the definition of the � − limit and cluster points and we will show their relation between those classes.

On generalized statistical convergence of double sequences via ideals

The concept of statistical convergence is one of the most active area of research in the field of summability. Most of the new summability methods have relation with this popular method. In this paper we generalize the notions of statistical convergence, (λ, μ)-statistical convergence, (V, λ, μ) summability and (C, 1, 1) summability for a double sequence x = (xjk) via ideals. We also establish the relation between our new methods.

Statistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function

The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.

Rates of convergence of certain King-type operators for functions with derivative of bounded variation

In this paper, we estimate the rates of pointwise approximation of certain King-type positive linear operators for functions with derivative of bounded variation. We also extend our results to the statistical approximation process via the concept of statistical convergence.

Statistical approximation by positive linear operators on modular spaces

In this paper, we investigate the problem of statistical approximation to a function by means of positive linear operators defined on a modular space. Especially, in order to get more powerful results than the classical aspects we mainly use the concept of statistical convergence. A non-trivial application is also presented.

On integral type generalizations of positive linear operators

We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute th

Statistically boundedness and statistical core of double sequences

The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Throughout this paper we will present multidimensional analogues of the results presented by Fridy and Orhan in 1997. To achieve this goal multidimensional analogues of the definition for bounded statistically sequences, statistical inferior and statistical superior will be presented. In addition to these results we will investigate statistical core for double sequences and study an inequality related to the statistical and P-cores of bounded double sequences.

Some results related with statistical convergence and Berezin symbols

The concept of discrete statistical Abel convergence is introduced. In terms of Berezin symbols we present necessary and sufficient condition under which a series ∑ n = 0 ∞ a n with bounded sequence { a n } n ⩾ 0 of complex numbers is discrete statistically Abel convergent. By using concept of statistical convergence we also give slight strengthening of a result of Gokhberg and Krein on compact operators.

Statistical gap Tauberian theorems in metric spaces

By using the concept of statistical convergence we present statistical Tauberian theorems of gap type for the Cesàro, Euler–Borel family and the Hausdorff families applicable in arbitrary metric spaces. In contrast to the classical gap Tauberian theorems, we show that such theorems exist in the statistical sense for the convolution methods which include the Taylor and the Borel matrix methods. We further provide statistical analogs of the gap Tauberian theorems for the Hausdorff methods and provide an explanation as to how the Tauberian rates over the gaps may differ from those of the classical Tauberian theorems.

Tauberian Theorems via Statistical Convergence

The concept of statistical convergence, which is related to the usual concept of convergence in probability, provides a regular summability method for abstract metric spaces. By using probabilistic tools, we provide some Tauberian theorems which have best possible order Tauberian conditions. Furthermore, these methods can be used to unify and improve the classical pointwise Tauberian theorems of summability theory for the random walk type methods as proved by Bingham, and Hausdorff methods as proved by Lorentz.

Statistical limit superior and limit inferior

Following the concept of statistical convergence and statistical cluster points of a sequence $x$, we give a definition of statistical limit superior and inferior which yields natural relationships among these ideas: e.g., $x$ is statistically convergent if and only if $\textrm {st}\text {-}\textrm {liminf} x= \textrm {st}\text {-}\textrm {limsup} x$. The statistical core of $x$ is also introduced, for which an analogue of Knopp’s Core Theorem is proved. Also, it is proved that a bounded sequence that is $C_{1}$-summable to its statistical limit superior is statistically convergent.