scholarly journals Generalized $A$-statistical convergence and a Korovkin type approximation theorem for double sequences

2013 ◽  
Vol 14 (1) ◽  
pp. 31
Author(s):  
Cemal Belen ◽  
Mustafa Yildirim
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation

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 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.

scholarly journals Korovkin-Type Theorems for ModularΨ-A-Statistical Convergence

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Carlo Bardaro ◽  
Antonio Boccuto ◽  
Kamil Demirci ◽  
Ilaria Mantellini ◽  
Sevda Orhan
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Orlicz Spaces ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Modular Spaces ◽  
New Type ◽  
Korovkin Type Theorems

We deal with a new type of statistical convergence for double sequences, calledΨ-A-statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our 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.

A Korovkin type approximation theorem in statistical sense

2006 ◽  
Vol 43 (3) ◽  
pp. 285-294 ◽  
Author(s):  
Esra Erkuş ◽  
Oktay Duman
Keyword(s):  
Compact Subset ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Dimensional Space ◽  
Linear Operators ◽  
Approximation Result ◽  
The Real ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Statistical Sense

In this study, using the concept of A-statistical convergence we investigate a Korovkin type approximation result for a sequence of positive linear operators defined on the space of all continuous real valued functions on any compact subset of the real m-dimensional space.

scholarly journals Korovkin type approximation theorem via AI2 -summability methods

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2663-2672
Author(s):  
Sudipta Dutta ◽  
Sevda Akdağ ◽  
Pratulananda Das
Keyword(s):  
Approximation Theorem ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Summability Methods

In this paper we consider the notion of AI2-summability for real double sequences which is an extension of the notion of AI-summability for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of AI2-summability.

scholarly journals TRIANGULAR A−STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS

2021 ◽  
pp. 065
Author(s):  
Selin Çınar
Keyword(s):  
Uniform Convergence ◽  
Approximation Theorem ◽  
Dimensional Space ◽  
Linear Operators ◽  
Two Dimensional ◽  
Double Sequences ◽  
The Real ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Relative Uniform Convergence

In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compactsubset of the real two-dimensional space. Based upon this new convergencemethod, we prove Korovkin-type approximation theorem. Finally, we give some further developments.

scholarly journals I_2-Relative uniform convergence and Korovkin type approximation

2021 ◽  
Vol 25 (2) ◽  
pp. 189-200
Author(s):  
Sevda Yildiz
Keyword(s):  
Uniform Convergence ◽  
Approximation Theorem ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Relative Uniform Convergence ◽  
New Type ◽  
First Time

In the present paper, an interesting type of convergence named ideal relative uniform convergence for double sequences of functions has been introduced for the first time. Then, the Korovkin type approximation theorem via this new type of convergence has been proved. An example to show that the new type of convergence is stronger than the convergence considered before has been given. Finally, the rate of  I2-relative uniform convergence has been computed.

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