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Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences

Richard F. Patterson and Ekrem Savaş

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 of Mathematics and Statistics
Volume 1 No. 2, 2005, 165-167

DOI: https://doi.org/10.3844/jmssp.2005.165.167

Published On: 30 June 2005

How to Cite: Patterson, R. F. & Savaş, E. (2005). Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences. Journal of Mathematics and Statistics, 1(2), 165-167. https://doi.org/10.3844/jmssp.2005.165.167

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Keywords

  • Double Lacunary Sequence
  • P-Convergent