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.

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 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.

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

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.

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 Statistical Korovkin and Voronovskaya type theorem for the Cesaro second-order operator of fuzzy numbers

2020 ◽  
Vol 65 (4) ◽  
pp. 561-574
Author(s):  
Naim L. Braha ◽  
Valdete Loku
Keyword(s):  
Rate Of Convergence ◽  
Fuzzy Numbers ◽  
Type Theorem ◽  
Summability Method ◽  
Second Order ◽  
Order Operator ◽  
Korovkin Type Theorem ◽  
Voronovskaya Type Theorem

In this paper we define the Ces\'aro second-order summability method for fuzzy numbers and prove Korovkin type theorem, then as the application of it, we prove the rate of convergence. In the last section, we prove the kind of Voronovskaya type theorem and give some concluding remarks related to the obtained results.

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