A remark on a modified Szász-Mirakjan operator

Guanzhen Zhou; Songping Zhou

Colloquium Mathematicae (1999)

  • Volume: 79, Issue: 2, page 157-160
  • ISSN: 0010-1354

Abstract

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We prove that, for a sequence of positive numbers δ(n), if n 1 / 2 δ ( n ) ¬ → ∞ as n → ∞ , 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.

How to cite

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Zhou, Guanzhen, and Zhou, Songping. "A remark on a modified Szász-Mirakjan operator." Colloquium Mathematicae 79.2 (1999): 157-160. <http://eudml.org/doc/210619>.

@article{Zhou1999,
abstract = {We prove that, for a sequence of positive numbers δ(n), if $n^\{1/2\}δ(n)\lnot \rightarrow \infty $ as $n\rightarrow \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.},
author = {Zhou, Guanzhen, Zhou, Songping},
journal = {Colloquium Mathematicae},
keywords = {modified Szász-Mirakjan operator; modified Szász-Mirakyan operator},
language = {eng},
number = {2},
pages = {157-160},
title = {A remark on a modified Szász-Mirakjan operator},
url = {http://eudml.org/doc/210619},
volume = {79},
year = {1999},
}

TY - JOUR
AU - Zhou, Guanzhen
AU - Zhou, Songping
TI - A remark on a modified Szász-Mirakjan operator
JO - Colloquium Mathematicae
PY - 1999
VL - 79
IS - 2
SP - 157
EP - 160
AB - We prove that, for a sequence of positive numbers δ(n), if $n^{1/2}δ(n)\lnot \rightarrow \infty $ as $n\rightarrow \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.
LA - eng
KW - modified Szász-Mirakjan operator; modified Szász-Mirakyan operator
UR - http://eudml.org/doc/210619
ER -

References

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  1. [1] J. Gróf, Über Approximation durch Polynome mit Belegungsfunktion, Acta Math. Acad. Sci. Hungar. 35 (1980), 109-116. Zbl0452.41017
  2. [2] T. Hermann, Approximation of unbounded functions on unbounded interval, ibid. 29 (1977), 393-398. Zbl0371.41012
  3. [3] H. G. Lehnhoff, On a modified Szász-Mirakjan-operator, J. Approx. Theory 42 (1984), 278-282. Zbl0573.41034
  4. [3] X. H. Sun, On the convergence of the modified Szász-Mirakjan operator, Approx. Theory Appl. 10 (1994), no. 1, 20-25. 

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