Statistical Convergence Of Double Sequences Research Articles

Generalized Weighted Statistical Convergence for Double Sequences of Fuzzy Numbers and Associated Korovkin-Type Approximation Theorem

We define the notions of weightedλ,μ-statistical convergence of orderγ1,γ2and strongly weightedλ,μ-summability ofγ1,γ2for fuzzy double sequences, where0<γ1,γ2≤1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weightedλ,μ-statistical convergence of orderγ1,γ2to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help ofq-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.

Korovkin Type Approximation Theorem for Functions of Two Variables Through αβ−Statistical Convergence

In this paper, we introduce the concepts of αβ−statistical convergence and strong αβ− summability of double sequences and investigate the relation between these two new concepts. Moreover, statistical convergence and αβ− statistical convergence of double sequences are compared under some certain assumptions. Finally, as an application, we prove Korovkin type approximation theorem for a function of two variables by using the notion of αβ−statistical convergence.

Statistical e-convergence of double sequences on probabilistic normed spaces

The concept of statistical convergence for double sequences on probabilistic normed spaces was presented by Karakus and Demirci in 2007. The purpose of this paper is to introduce the concept of statistical e-convergence for double sequences and study some fundamental properties of statistical e-convergence for double sequences on probabilistic normed spaces.

Statistical convergence of double sequences on product time scales

Abstract In this study, we present the basic concepts of statistical convergence for double sequences on an arbitrary product time scale. Moreover, we investigate the connection between statistical convergence for double sequences and double Cesàro summability on a product time scale.

Lacunary invariant statistical convergence of double sequences of sets

In this paper, we introduce the concepts of Wijsman invariant convergence, Wijsman invariant statistical convergence, Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence for double sequences of sets. Also, we investigate existence of some relations among these new convergence concepts for double sequences of sets.

On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces

On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces

Rough $I$-statistical convergence of double sequences in normed linear spaces

Rough $I$-statistical convergence of double sequences in normed linear spaces

Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

We introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy and strongly (λ, µ)p-summable double sequences in a paranormed space and obtain their relationship with (λ, µ)- statistical convergence.

On the Lacunary (A, φ)-Statistical Convergence of Double Sequences

We extend some results known from the literature for ordinary (single) sequences to multiple sequences of real numbers. Further, we introduce a concept of double lacunary strong (A, φ) -convergence with respect to a modulus function. In addition, we also study some relationships between double lacunary strong (A, φ) -convergence with respect to a modulus and double lacunary statistical convergence.

Rough {I}_{2}-lacunary statistical convergence of double sequences

In this paper, we introduce and study the notion of rough mathcal {I}_{2}-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough mathcal{I}_{2}-lacunary statistical limit set of a double sequence and discuss some properties of this set.

Weighted Statistical Convergence of Double Sequences in Non-Archimedean Fields

Let K be a complete, non-trivially valued non-archimedean field. In this paper, weighted statistical convergence and statistical summability of double sequences are studied. Also the notion of (, p, q) - summability and inclusion relations have been discussed in such fields.

F_{(lambda,mu)}-statistical convergence of order \u03b1\u0303 for double sequences

New concepts of f_{lambda,mu }-statistical convergence for double sequences of order α̃ and strong f_{lambda,mu }-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we give the relationship between the spaces w_{tilde{alpha },0}^{2} ( f,lambda,mu ), w_{tilde{alpha }}^{2} ( f,lambda,mu ) and w_{tilde{alpha},infty }^{2} ( f,lambda,mu ). Then we express the properties of strong f_{lambda,mu }-Cesàro summability of order β̃ which is related to strong f_{lambda,mu }-Cesàro summability of order α̃. Also, some relations between f_{lambda,mu }-statistical convergence of order α̃ and strong f_{lambda,mu }-Cesàro summability of order α̃ are given.

On statistical convergence of double sequences of fuzzy valued functions

On statistical convergence of double sequences of fuzzy valued functions

ON DOUBLE WEIGHTED MEAN STATISTICAL CONVERGENCE

In this paper, we have established some new theorems on double weighted mean statistical convergence of double sequences, which gives some new results and generalizes the some previous known results of Karakaya.

Generalized weighted statistical convergence of double sequences and applications

In this paper we introduce the concept generalized weighted statistical convergence of double sequences. Some relations between weighted (?,?)-statistical convergence and strong (N???,p,q,?,?)-summablity of double sequences are examined. Furthemore, we apply our new summability method to prove a Korovkin type theorem.

Weighted lacunary statistical convergence of double sequences in locally solid Riesz spaces

Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Ba?ar?r and Konca [7]. In this work, we define and study weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.

On statistical convergence of double sequences of closed sets

In this paper, we introduce the concepts of statistical inner and statistical outer limits for double sequences of closed sets and give some formulas for finding these limits. Also, we give the Kuratowski statistical convergence of double sequences of sets by means of the statistical inner and statistical outer limits of a double sequence of closed sets.

Lacunary statistical convergence of double sequences of sets

In this paper, we study the concepts of Wijsman statistical convergence, Wijsman lacunary statistical convergence, Wijsman lacunary convergence and Wijsman strongly lacunary convergence double sequences of sets and investigate the relationship among them.

On rough statistical convergence of double sequences in normed linear spaces

The idea of rough statistical convergence for single sequences was introduced by Salih Aytar as a generalization of rough convergence. In this paper we define and study rough statistical convergence of double sequences, the set of rough statistical limits of a double sequence. We also study the relation between the set of statistical cluster points and the set of rough limit points of a double sequence.

Triangular A-Statistical Approximation by Double Sequences of Positive Linear Operators

In the present paper we introduce a new type of statistical convergence for double sequences called triangular A-statistical convergence and we show that triangular A-statistical convergence and A-statistical convergence overlap, neither contains the other. Also, we give a Korovkin-type approximation theorem using this new type of convergence. Finally we give some further developments.