# Lacunary equi-statistical convergence of positive linear operators

Open Mathematics (2009)

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

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topHüseyin 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 -

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