Statistical Korovkin-type theory for matrix-valued functions

2011 ◽  
Vol 48 (4) ◽  
pp. 489-508
Author(s):  
Oktay Duman ◽  
Esra Erkuş-Duman
Keyword(s):  
Type Theory ◽  
Statistical Convergence ◽  
Toeplitz Matrices ◽  
Type Theorem ◽  
Positive Operators ◽  
Korovkin Type Theorem ◽  
Linear Positive Operators ◽  
Numer Anal ◽  
Matrix Spaces

In this paper, using the notion of A-statistical convergence from the summability theory, we obtain a Korovkin-type theorem for the approximation by means of matrixvalued linear positive operators. We show that our theorem is more applicable than the result introduced by S. Serra-Capizzano [A Korovkin based approximation of multilevel Toeplitz matrices (with rectangular unstructured blocks) via multilevel trigonometric matrix spaces, SIAM J. Numer. Anal., 36 (1999), 1831–1857]. Furthermore, we compute the A-statistical rates of our approximation.

scholarly journals A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

2020 ◽  
Vol 13 (5) ◽  
pp. 1212-1230
Author(s):  
Susanta Kumar Paikray ◽  
Priyadarsini Parida ◽  
S. A. Mohiuddine
Keyword(s):  
Statistical Convergence ◽  
Type Theorem ◽  
Point Of View ◽  
Scale Function ◽  
Korovkin Type Theorem ◽  
Approximation Theorems ◽  
Fuzzy Approximation ◽  
Inclusion Relations ◽  
Korovkin Type Theorems ◽  
Sequence Of Functions

The aim of this paper is to introduce the notions of relatively deferred Nörlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Nörlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaidnotions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

Some properties of modified Szász–Mirakyan operators in polynomial spaces via the power summability method

2020 ◽  
Vol 26 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Naim L. Braha
Keyword(s):  
Statistical Convergence ◽  
Type Theorem ◽  
Summability Method ◽  
Korovkin Type Theorem ◽  
Summability Methods ◽  
Voronovskaya Type Theorem

AbstractIn this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A-statistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss–Voronovskaya type theorem.

scholarly journals The Voronovskaja theorem for some linear positive operators defined by infinite sum

2011 ◽  
Vol 20 (1) ◽  
pp. 55-61
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Type Theorem ◽  
Positive Operators ◽  
Linear Positive Operators ◽  
Szász Operators ◽  
Voronovskaja Type Theorem ◽  
Infinite Sum

The main goal of this paper is to establish a Voronovskaja type theorem for the Szasz-Mirakjan-Schurer operators. As a particular case, we get also the Voronovskaja type theorem for the well known Mirakjan-Favard-Szasz operators.

scholarly journals About Some Linear Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-13
Author(s):  
Ovidiu T. Pop
Keyword(s):  
Rate Of Convergence ◽  
General Class ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Linear Operators ◽  
Linear Positive Operators ◽  
Voronovskaja Type Theorem

Using the method of Jakimovski and Leviatan from their work in 1969, we construct a general class of linear positive operators. We study the convergence, the evaluation for the rate of convergence in terms of the first modulus of smoothness and we give a Voronovskaja-type theorem for these operators.

scholarly journals Generalized weighted statistical convergence of double sequences and applications

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 753-762 ◽  
Author(s):  
Muhammed Cinar ◽  
Mikail Et
Keyword(s):  
Statistical Convergence ◽  
Type Theorem ◽  
Summability Method ◽  
Double Sequences ◽  
Korovkin Type Theorem

In this paper we introduce the concept generalized weighted statistical convergence of double sequences. Some relations between weighted (?,?)-statistical convergence and strong (N???,p,q,?,?)-summablity of double sequences are examined. Furthemore, we apply our new summability method to prove a Korovkin type theorem.

Korovkin type theorem for linear k-positive operators in a polydisc of analytical functions

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
Akif D. Gadjiev ◽  
Rashid A. Aliev
Keyword(s):  
Type Theorem ◽  
Positive Operators ◽  
Korovkin Type Theorem ◽  
Analytical Functions

AbstractIn this work we obtained Korovkin type theorem for linear

scholarly journals Some Properties of Kantorovich-Stancu-Type Generalization of Szász Operators including Brenke-Type Polynomials via Power Series Summability Method

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Naim Latif Braha ◽  
Toufik Mansour ◽  
Mohammad Mursaleen
Keyword(s):  
Power Series ◽  
Statistical Convergence ◽  
Type Theorem ◽  
Summability Method ◽  
Korovkin Type Theorem ◽  
Szász Operators

In this paper, we study the Kantorovich-Stancu-type generalization of Szász-Mirakyan operators including Brenke-type polynomials and prove a Korovkin-type theorem via the T-statistical convergence and power series summability method. Moreover, we determine the rate of the convergence. Furthermore, we establish the Voronovskaya- and Grüss-Voronovskaya-type theorems for T-statistical convergence.

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

Sign in / Sign up

Export Citation Format

Share Document