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 Properties of Generalized λ -Bernstein–Stancu-Type Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Qing-Bo Cai ◽  
Gülten Torun ◽  
Ülkü Dinlemez Kantar
Keyword(s):  
Asymptotic Behavior ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Approximation Properties ◽  
Numerical Examples ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Voronovskaja Type Theorem

The present study introduces generalized λ -Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of G m , λ α , β f , x to f x with respect to m values.

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.

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.

scholarly journals Some approximation results for (p,q)-Lupaş-Schurer operators

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 217-229 ◽  
Author(s):  
K. Kanat ◽  
M. Sofyalıoğlu
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation

In this paper, we introduce Lupa?-Schurer operators based on (p,q)-integers. Then, we deal with the approximation properties for (p,q)-Lupa?-Schurer operators based on Korovkin type approximation theorem. Moreover, we compute rate of convergence by using modulus of continuity, with the help of functions of Lipschitz class and Peetre?s K-functionals.

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 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.

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