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.

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.

The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fadime Dirik ◽  
Kamil Demirci ◽  
Sevda Yıldız ◽  
Ana Maria Acu
Keyword(s):  
Uniform Convergence ◽  
Approximation Theorem ◽  
Double Sequence ◽  
Korovkin Theorem ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation ◽  
The Korovkin Theorem ◽  
Korovkin Type Approximation Theorems ◽  
Sequence Of Functions

AbstractIn this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.

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 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.

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 Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 316 ◽  
Author(s):  
Hari Srivastava ◽  
Faruk Özger ◽  
S. Mohiuddine
Keyword(s):  
Uniform Convergence ◽  
Shape Parameter ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Bernstein Operators ◽  
Global Approximation ◽  
Approximation Result ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Direct Approximation

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ - 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.

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 A Korovkin Type Approximation Theorem and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Malik Saad Al-Muhja
Keyword(s):  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Stieltjes Integral ◽  
Periodic Functions ◽  
Third Order ◽  
Korovkin Type Approximation Theorem ◽  
The Third ◽  
Type Approximation ◽  
Statistical Limit

We present a Korovkin type approximation theorem for a sequence of positive linear operators defined on the space of all real valued continuous and periodic functions viaA-statistical approximation, for the rate of the third order Ditzian-Totik modulus of smoothness. Finally, we obtain an interleave between Riesz's representation theory and Lebesgue-Stieltjes integral-i, for Riesz's functional supremum formula via statistical limit.

scholarly journals Korovkin-type approximation theorem for Bernstein Stancu operator of rough statistical convergence of triple sequence

2019 ◽  
Vol 38 (7) ◽  
pp. 69-83
Author(s):  
Ayten Esi ◽  
Mustafa Kemal Ozdemir ◽  
Nagarajan Subramanian
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Increasing Function

We obtain a Korovkin-type approximation theorem for Bernstein Stancu polynomials of rough statistical convergence of triple sequences of positive linear operators of three variables from $H_{\omega}\left( K\right) $ to $C_{B}\left( K\right) $, where $K=[0,\infty)\times\lbrack0,\infty )\times\lbrack0,\infty)$ and $\omega$ is non-negative increasing function on $K$.

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