Four-dimensional matrix transformation and rate of A -statistical convergence of periodic functions

In this paper, using the concept of A -statistical convergence for double real sequences, we obtain a Korovkin type-approximation theorem for double sequences of positive linear operators defined on the space of all 2 π -periodic and real valued continuous functions on the real two-dimensional space...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 52; no. 9; pp. 1858 - 1866
Main Authors: Demirci, Kamil, Dirik, Fadime
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.11.2010
Elsevier
Subjects:
[formula omitted]-periodic and real valued continuous functions
Acceleration of convergence
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Operator theory
Rates of [formula omitted]-statistical convergence for double sequences
Regularity for double sequences
Sciences and techniques of general use
The Korovkin type-approximation theorem
2 π -periodic and real valued continuous functions
Rates of A -statistical convergence for double sequences
The Korovkin type-approximation theorem
Regularity for double sequences
Two dimensional space
2π-periodic and real valued continuous functions
Approximation
Convergence acceleration
Periodic function
Continuous function
Linear operator
Convergence
Numerical analysis
Real sequence
Real function
Applied mathematics
Convergence rate
Rates ofA-statistical convergence for double sequences
Approximation theory
Mathematical model
Computer aided analysis
Positive operator
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:In this paper, using the concept of A -statistical convergence for double real sequences, we obtain a Korovkin type-approximation theorem for double sequences of positive linear operators defined on the space of all 2 π -periodic and real valued continuous functions on the real two-dimensional space. Furthermore, we display an application which shows that our new result is stronger than its classical version. Also, we study rates of A -statistical convergence of a double sequence of positive linear operators acting on this space. Finally, displaying an example, it is shown that our statistical rates are more efficient than the classical aspects in the approximation theory.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2010.07.015