Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu; Halil Gezer

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 558-567
  • ISSN: 2391-5455

Abstract

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In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.

How to cite

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Hüseyin Aktuğlu, and Halil Gezer. "Lacunary equi-statistical convergence of positive linear operators." Open Mathematics 7.3 (2009): 558-567. <http://eudml.org/doc/268986>.

@article{HüseyinAktuğlu2009,
abstract = {In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.},
author = {Hüseyin Aktuğlu, Halil Gezer},
journal = {Open Mathematics},
keywords = {Statistical convergence; Lacunary statistical convergence; A-statistical convergence; Equi-statistical convergence; Korovkin type approximation theorem; Order of convergence; statistical convergence; lacunary statistical convergence; equi-statistical convergence; order of convergence},
language = {eng},
number = {3},
pages = {558-567},
title = {Lacunary equi-statistical convergence of positive linear operators},
url = {http://eudml.org/doc/268986},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Hüseyin Aktuğlu
AU - Halil Gezer
TI - Lacunary equi-statistical convergence of positive linear operators
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 558
EP - 567
AB - In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.
LA - eng
KW - Statistical convergence; Lacunary statistical convergence; A-statistical convergence; Equi-statistical convergence; Korovkin type approximation theorem; Order of convergence; statistical convergence; lacunary statistical convergence; equi-statistical convergence; order of convergence
UR - http://eudml.org/doc/268986
ER -

References

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