Journal of Mathematics and Statistics

Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences

Richard F. Patterson and Ekrem Savas

DOI : 10.3844/jmssp.2005.165.167

Journal of Mathematics and Statistics

Volume 1, Issue 2

Pages 165-167


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}.


© 2005 Richard F. Patterson and Ekrem Savas. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.