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Title: Remarks on an article of J.P. King (English)
Author: Gonska, Heiner
Author: Piţul, Paula
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 46
Issue: 4
Year: 2005
Pages: 645-652
Category: math
Summary: 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. (English)
Keyword: positive linear operators
Keyword: degree of approximation
Keyword: contraction principle
Keyword: second order modulus
Keyword: second moments
MSC: 41A25
MSC: 41A36
MSC: 47H10
idZBL: Zbl 1121.41013
idMR: MR2259496
Date available: 2009-05-05T16:54:02Z
Last updated: 2012-04-30
Stable URL:
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Reference: [4] King P.J.: Positive linear operators which preserve $x^2$.Acta Math. Hungar. 99 (2003), 203-208. MR 1973095
Reference: [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. MR 0110017
Reference: [6] Păltănea R.: Approximation by linear positive operators: Estimates with second order moduli.Ed. Univ. Transilvania, Braşov, 2003.
Reference: [7] Rus I.A.: Iterates of Bernstein operators, via contraction principle.J. Math. Anal. Appl. 292 (2004), 259-261. Zbl 1056.41004, MR 2050229
Reference: [8] Shisha O., Mond B.: The degree of convergence of linear positive operators.Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1196-1200. MR 0230016


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