Statistical approximation to Bögel-type continuous and periodic functions

Fadime Dirik; Oktay Duman; Kamil Demirci

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 539-549
  • ISSN: 2391-5455

Abstract

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In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.

How to cite

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Fadime Dirik, Oktay Duman, and Kamil Demirci. "Statistical approximation to Bögel-type continuous and periodic functions." Open Mathematics 7.3 (2009): 539-549. <http://eudml.org/doc/269340>.

@article{FadimeDirik2009,
abstract = {In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.},
author = {Fadime Dirik, Oktay Duman, Kamil Demirci},
journal = {Open Mathematics},
keywords = {The Korovkin theorem; B-continuous functions; B-2π-periodic functions; A-statistical convergence for double sequences; Regularity for double sequences; Korovkin theorem; -continuous functions; -periodic functions; -statistical convergence for double sequences; regularity for double sequences},
language = {eng},
number = {3},
pages = {539-549},
title = {Statistical approximation to Bögel-type continuous and periodic functions},
url = {http://eudml.org/doc/269340},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Fadime Dirik
AU - Oktay Duman
AU - Kamil Demirci
TI - Statistical approximation to Bögel-type continuous and periodic functions
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 539
EP - 549
AB - In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.
LA - eng
KW - The Korovkin theorem; B-continuous functions; B-2π-periodic functions; A-statistical convergence for double sequences; Regularity for double sequences; Korovkin theorem; -continuous functions; -periodic functions; -statistical convergence for double sequences; regularity for double sequences
UR - http://eudml.org/doc/269340
ER -

References

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