@article {10.3844/jmssp.2005.165.167,
article_type = {journal},
title = {Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences},
author = {Patterson, Richard F. and Savaş, Ekrem},
volume = {1},
year = {2005},
month = {Jun},
pages = {165-167},
doi = {10.3844/jmssp.2005.165.167},
url = {https://thescipub.com/abstract/jmssp.2005.165.167},
abstract = {In this study we shall extended Korovkin and Weierstrass approximation theorem to
lacunary statistical convergent sequences. In addition, to these approximation theorems, we established
also introduced lacunary statistically convergent of degree β and establish a corresponding Korovkin
type theorem namely the following:
If the sequence of positive linear operators Pn: CM [a, b]→ B[a, b] satisfies the conditions:
* ||Pn(1, x)-1||β→0(Sβ1θ ) as r→ ∞,
* ||Pn(t, x)-x||B→0(Sβ2θ  ) as r→ ∞ and
* ||Pn(t2, x)-x2||B→0(Sβ3θ ) as r→ ∞, then for any function f ∈ CM [a, b], we have ||Pn (f, x)-
(x)||B→0(Sβθ ) as r→ ∞ and β = min{β1, β2, β3}.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}