Remarks on an article of J.P. King

Heiner Gonska; Paula Piţul

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 4, page 645-652
  • ISSN: 0010-2628

Abstract

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The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized.

How to cite

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Gonska, Heiner, and Piţul, Paula. "Remarks on an article of J.P. King." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 645-652. <http://eudml.org/doc/249520>.

@article{Gonska2005,
abstract = {The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized.},
author = {Gonska, Heiner, Piţul, Paula},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {positive linear operators; degree of approximation; contraction principle; second order modulus; second moments; positive linear operators; degree of approximation},
language = {eng},
number = {4},
pages = {645-652},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remarks on an article of J.P. King},
url = {http://eudml.org/doc/249520},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Gonska, Heiner
AU - Piţul, Paula
TI - Remarks on an article of J.P. King
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 645
EP - 652
AB - The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized.
LA - eng
KW - positive linear operators; degree of approximation; contraction principle; second order modulus; second moments; positive linear operators; degree of approximation
UR - http://eudml.org/doc/249520
ER -

References

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  1. Agratini O., Rus I.A., Iterates of a class of discrete linear operators, Comment. Math. Univ. Carolinae 44 (2003), 555-563. (2003) Zbl1096.41015MR2025820
  2. Beresin I.S., Zhidkov N.P., Numerische Methoden II, VEB Deutscher Verlag der Wissenschaften, Berlin, 1971. 
  3. Kelisky R.P., Rivlin T.J., Iterates of Bernstein polynomials, Pacific J. Math. 21 (1967), 511-520. (1967) Zbl0177.31302MR0212457
  4. King P.J., Positive linear operators which preserve x 2 , Acta Math. Hungar. 99 (2003), 203-208. (2003) MR1973095
  5. Mamedov R.G., On the order of approximation of functions by sequences of linear positive operators (Russian), Dokl. Akad. Nauk SSSR 128 (1959), 674-676. (1959) MR0110017
  6. Păltănea R., Approximation by linear positive operators: Estimates with second order moduli, Ed. Univ. Transilvania, Braşov, 2003. 
  7. Rus I.A., Iterates of Bernstein operators, via contraction principle, J. Math. Anal. Appl. 292 (2004), 259-261. (2004) Zbl1056.41004MR2050229
  8. Shisha O., Mond B., The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1196-1200. (1968) MR0230016

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