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A remark on a modified Szász-Mirakjan operator

100%

Zhou G., Zhou S.

Colloquium Mathematicum

1999

tom 79

nr 2

157-160

We prove that, for a sequence of positive numbers δ(n), if $n^{1/2}δ(n)\not\to\infty$ as $n\to\infty$, to guarantee that the modified Szász-Mirakjan operators $S_{n,δ}(f,x)$ converge to f(x) at every point, f must be identically zero.

On $L^{p}$ integrability and convergence of trigonometric series

81%

Yu D., Zhou P., Zhou S.

Studia Mathematica

2007

tom 182

nr 3

215-226

We first give a necessary and sufficient condition for $x^{-γ} ϕ(x) ∈ L^{p}$, 1 < p < ∞, 1/p - 1 < γ < 1/p, where ϕ(x) is the sum of either $∑_{k=1}^{∞} a_{k} cos kx$ or $∑_{k=1}^{∞} b_{k} sin kx$, under the condition that {λₙ} (where λₙ is aₙ or bₙ respectively) belongs to the class of so called Mean Value Bounded Variation Sequences (MVBVS). Then we discuss the relations among the Fourier coefficients λₙ and the sum function ϕ(x) under the condition that {λₙ} ∈ MVBVS, and deduce a sharp estimate for the weighted modulus of continuity of ϕ(x) in $L^{p}$ norm.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Zhou S.

1 Yu D.

1 Zhou G.

1 Zhou P.

1 2007

1 1999

Wyniki wyszukiwania

A remark on a modified Szász-Mirakjan operator

On $L^{p}$ integrability and convergence of trigonometric series