scholarly journals Korovkin type theorem for functions of two variables via lacunary equistatistical convergence

2017 ◽  
Vol 102 (116) ◽  
pp. 203-209
Author(s):  
M. Mursaleen
Keyword(s):  
Pointwise Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Test Functions ◽  
Korovkin Type Theorem ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

Aktu?lu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and G?n?l [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, x/1+x, y/1+y, (x/1+x)2 +(y/1+y)2. We apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem for functions of two variables by using test functions 1, x/1?x, y/1?y, (x/1?x)2+(y/1?y)2.

scholarly journals A Spline Group – Korovkin Approximation Theorem

2015 ◽  
Vol 7 (2) ◽  
pp. 110
Author(s):  
Malik Saad Al-Muhja
Keyword(s):  
Linear Operator ◽  
Approximation Theorem ◽  
Positive Linear Operator ◽  
Homogeneous Groups ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

In this paper, using homogeneous groups, we prove a Korovkin type approximation theorem for a spline groupby using the notion of a generalization of positive linear operator.

scholarly journals Korovkin type approximation theorems via lacunary equistatistical convergence

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3641-3647 ◽  
Author(s):  
Abdullah Alotaibi ◽  
M. Mursaleen
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Approximation Theorem ◽  
Test Functions ◽  
Central European ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Korovkin Type Approximation Theorems

Aktu?lu and H. Gezer [Central European J. Math. 7 (2009), 558-567] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. In this paper, we apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem by using test functions 1, x/1-x,(x/1-x)2.

scholarly journals Statistical αβ-summability and Korovkin type approximation theorem

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3483-3491 ◽  
Author(s):  
Ali Karaisa
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Bernstein Operator ◽  
Inclusion Relation ◽  
Korovkin Type Theorem ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Summability Methods

In this study, we define [N?,??]q - summability and statistical (N?,??) summability. We also establish some inclusion relation and some related results for this new summability methods. Further we apply Korovkin type approximation theorem through statistical (N?,??) summability and we apply the classical Bernstein operator to construct an example in support of our result. Furthermore, we present a rate of convergence which is uniform in Korovkin type theorem by statistical (N?,??) summability.

scholarly journals Approximation Theorems for Functions of Two Variables viaσ-Convergence

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mohammed A. Alghamdi
Keyword(s):  
Approximation Theorem ◽  
Bernstein Polynomials ◽  
Test Functions ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Functions Of Two Variables

Çakan et al. (2006) introduced the concept ofσ-convergence for double sequences. In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1,x,y, andx2+y2and construct an example by considering the Bernstein polynomials of two variables in support of our main result.

scholarly journals Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 636 ◽  
Author(s):  
Hari Mohan Srivastava ◽  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray
Keyword(s):  
Banach Space ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Real Sequence ◽  
Test Functions ◽  
Real Numbers ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Algebraic Test

The concept of the deferred Nörlund equi-statistical convergence was introduced and studied by Srivastava et al. [Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112 (2018), 1487–1501]. In the present paper, we have studied the notion of the deferred Nörlund statistical convergence and the statistical deferred Nörlund summability for sequences of real numbers defined over a Banach space. We have also established a theorem presenting a connection between these two interesting notions. Moreover, based upon our proposed methods, we have proved a new Korovkin-type approximation theorem with algebraic test functions for a sequence of real numbers on a Banach space and demonstrated that our theorem effectively extends and improves most of the earlier existing results (in classical and statistical versions). Finally, we have presented an example involving the generalized Meyer–König and Zeller operators of a real sequence demonstrating that our theorem is a stronger approach than its classical and statistical versions.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Approximation Theorem ◽  
Bernstein Operators ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables ◽  
Sequences Of Fuzzy Numbers ◽  
Bivariate Functions

We define the notions of weighted λ,μ-statistical convergence of order γ1,γ2 and strongly weighted λ,μ-summability of γ1,γ2 for fuzzy double sequences, where 0<γ1,γ2≤1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted λ,μ-statistical convergence of order γ1,γ2 to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of q-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.

scholarly journals A certain class of statistical probability convergence and its applications to approximation theorems

2020 ◽  
pp. 39-39
Author(s):  
H.M. Srivastava ◽  
Bidu Jena ◽  
Susanta Paikray
Keyword(s):  
Banach Space ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Random Variables ◽  
Test Functions ◽  
Convolution Operators ◽  
Statistical Probability ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation

In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the concept of statistical convergence for sequences of real numbers, which are defined over a Banach space via deferred weighted summability mean. We first establish a theorem presenting a connection between them. Based upon our proposed methods, we then prove a new Korovkin-type approximation theorem with periodic test functions for a sequence of random variables on a Banach space and demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results (in statistical versions). We also estimate the rate of deferred weighted statistical probability convergence and accordingly establish a new result. Finally, an illustrative example is presented here by means of the generalized Fej?r convolution operators of a sequence of random variables in order to demonstrate that our established theorem is stronger than its traditional and statistical versions.

scholarly journals Statistical σ-convergence of double sequences with application

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2783-2792
Author(s):  
M. Mursaleen ◽  
Cemal Belen ◽  
Syed Rizvi
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Invariant Mean ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables

The concepts of ?-statistical convergence, statistical ?-convergence and strong ?q-convergence of single (ordinary) sequences have been introduced and studied in [M. Mursaleen, O.H.H. Edely, On the invariant mean and statistical convergence, App. Math. Lett. 22, (2011), 1700-1704] which were obtained by unifying the notions of density and invariant mean. In this paper, we extend these ideas from single to double sequences. We also use the concept of statistical ?-convergence of double sequences to prove a Korovkin-type approximation theorem for functions of two variables and give an example to show that our Korovkin-type approximation theorem is stronger than those proved earlier by other authors.

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