Statistical Approximation of Positive Linear Operators

2014 ◽  
pp. 133-148
Author(s):  
M. Mursaleen ◽  
S. A. Mohiuddine
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Deferred weighted 𝒜-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems

2018 ◽  
Vol 24 (1) ◽  
pp. 1-16 ◽  
Author(s):  
H. M. Srivastava ◽  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray ◽  
U. K. Misra
Keyword(s):  
Statistical Convergence ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Lagrange Polynomials ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Special Cases ◽  
Korovkin Type Approximation Theorems ◽  
Appl Math

AbstractRecently, the notion of positive linear operators by means of basic (orq-) Lagrange polynomials and{\mathcal{A}}-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means ofq-Lagrange polynomials andA-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911–6918]. In our present investigation, we introduce a certain deferred weighted{\mathcal{A}}-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1,tand{t^{2}}defined on a Banach space{C[0,1]}for a sequence of (presumably new) positive linear operators based upon{(p,q)}-Lagrange polynomials. Furthermore, we investigate the deferred weighted{\mathcal{A}}-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

Statistical approximation by positive linear operators on modular spaces

Positivity ◽  
2009 ◽  
Vol 14 (2) ◽  
pp. 321-334 ◽  
Author(s):  
Sevda Karakuş ◽  
Kamil Demirci ◽  
Oktay Duman
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Modular Spaces

Statistical Approximation Properties of Some Positive Linear Operators

2021 ◽  
Author(s):  
Faruk Özger
Keyword(s):  
Functional Analysis ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Important Concept ◽  
Short Survey

Statistical convergence is an important concept in functional analysis. In this work, we give a short survey about statistical convergence and statistical convergence of some positive linear operators to approximate functions.

Triangular A-Statistical Approximation by Double Sequences of Positive Linear Operators

2015 ◽  
Vol 68 (3-4) ◽  
pp. 271-291 ◽  
Author(s):  
C. Bardaro ◽  
A. Boccuto ◽  
K. Demirci ◽  
I. Mantellini ◽  
S. Orhan
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Double Sequences ◽  
Statistical Approximation
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