A remark on a modified Szász-Mirakjan operator

• Autorzy: Guanzhen Zhou , Songping Zhou
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

modified Szász-Mirakjan operator

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 79
• Numer: 2
• Strony: 157-160

Daty

wydano

1999

otrzymano

1998-03-098

Twórcy

autor

Guanzhen Zhou

• Department of Mathematics Ningbo University, Ningbo, Zhejiang 315211, China

autor

Songping Zhou

• State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation, Southwest Institute of Petroleum, Nangchong, Sichuan 637001 China

Bibliografia

• [1] J. Gróf, Über Approximation durch Polynome mit Belegungsfunktion, Acta Math. Acad. Sci. Hungar. 35 (1980), 109-116.
• [2] T. Hermann, Approximation of unbounded functions on unbounded interval, ibid. 29 (1977), 393-398.
• [3] H. G. Lehnhoff, On a modified Szász-Mirakjan-operator, J. Approx. Theory 42 (1984), 278-282.
• [3] X. H. Sun, On the convergence of the modified Szász-Mirakjan operator, Approx. Theory Appl. 10 (1994), no. 1, 20-25.