Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences | Science Publications

摘要

> 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 P_n: C_M [a, b]→ B[a, b] satisfies the conditions: * ||P_n(1, x)-1||_β→0(Sβ1_θ ) as r→ ∞, * ||P_n(t, x)-x||_B→0(Sβ2_θ ) as r→ ∞ and * ||P_n(t2, x)-x2||_B→0(Sβ3_θ ) as r→ ∞, then for any function f ∈ C_M [a, b], we have ||P_n (f, x)- (x)||_B→0(Sβ_θ ) as r→ ∞ and β = min{β₁, β₂, β₃}. Key words: Double Lacunary Sequence, P-Convergent