scholarly journals Korovkin type approximation for double sequences via statistical A-summation process on modular spaces

2018 ◽  
Vol 63 (1) ◽  
pp. 125-140
Author(s):  
Sevda Orhan ◽  
Burçak Kolay
Keyword(s):  
Double Sequences ◽  
Type Approximation ◽  
Modular Spaces ◽  
Summation Process

scholarly journals ABSTRACT KOROVKIN THEOREMS VIA RELATIVE MODULAR CONVERGENCE FOR DOUBLE SEQUENCES OF LINEAR OPERATORS

2020 ◽  
pp. 561
Author(s):  
Sevda Yıldız ◽  
Kamil Demirci
Keyword(s):  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Double Sequences ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Modular Spaces ◽  
Abstract Version ◽  
Modular Convergence ◽  
Korovkin Type Approximation Theorems

We will obtain an abstract version of the Korovkin type approximation theorems with respect to the concept of statistical relative convergence in modular spaces for double sequences of positive linear operators. We will give an application showing that our results are stronger than classical ones. We will also study an extension to non-positive operators.

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.

A-summation process and Korovkin-type approximation theorem for double sequences of positive linear operators

2012 ◽  
Vol 62 (2) ◽  
Author(s):  
Sevda Karakuş ◽  
Kami̇l Demi̇rci̇
Keyword(s):  
Approximation Theorem ◽  
Dimensional Space ◽  
Rates Of Convergence ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Two Dimensional ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Summation Process

AbstractThe aim of this paper is to present a Korovkin-type approximation theorem on the space of all continuous real valued functions on any compact subset of the real two-dimensional space by using a A-summation process. We also study the rates of convergence of positive linear operators with the help of the modulus of continuity.

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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