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.
@article{bwmeta1.element.doi-10_2478_s11533-009-0009-4,
author = {H\"useyin Aktu\u glu and Halil Gezer},
title = {Lacunary equi-statistical convergence of positive linear operators},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {558-567},
zbl = {1181.41039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0009-4}
}
Hüseyin Aktuğlu; Halil Gezer. Lacunary equi-statistical convergence of positive linear operators. Open Mathematics, Tome 7 (2009) pp. 558-567. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0009-4/
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