TY  - JOUR
AU  - Patterson, Richard F. 
AU  - Savaş, Ekrem 
PY  - 2005
TI  - Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences
JF  - Journal of Mathematics and Statistics
VL  - 1
IS  - 2
DO  - 10.3844/jmssp.2005.165.167
UR  - https://thescipub.com/abstract/jmssp.2005.165.167
AB  - 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}.