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.

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.

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 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.

scholarly journals Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4549-4560 ◽  
Author(s):  
S.A. Mohiuddine ◽  
Bipan Hazarika ◽  
Mohammed Alghamdi
Keyword(s):  
Uniform Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Korovkin Theorem ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Convergence Of Sequences ◽  
Relative Uniform Convergence ◽  
Relatively Uniform Convergence

We introduce the notion of ideally relative uniform convergence of sequences of real valued functions. We then apply this notion to prove Korovkin-type approximation theorem, and then construct an illustrative example by taking (p,q)-Bernstein operators which proves that our Korovkin theorem is stronger than its classical version as well as statistical relative uniform convergence. The rate of ideal relatively uniform convergence of positive linear operators by means of modulus of continuity is calculated. Finally, the Voronovskaya-type approximation theorem is also investigated.

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 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.

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