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The degree of approximation by positive operators on compact connected abelian groups

Part of: Approximations and expansions

Published online by Cambridge University Press:  09 April 2009

Walter R. Bloom  and
Joseph F. Sussich
Walter R. Bloom
Affiliation:
School of Mathematical and Physical SciencesMurdoch UniversityPerth, WesternAustralia6150
Joseph F. Sussich
Affiliation:
School of Mathematical and Physical SciencesMurdoch UniversityPerth, WesternAustralia6150
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Abstract

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In 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2 π-periodic functions and lim Tnf = f uniformly for f = 1, cos and sin, then lim Tnf = f uniformly for all f ∈ C. Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of f. We extend this result by giving a quantitative version of Korovkin's theorem for compact connected abelian groups.

MSC classification

Secondary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A36: Approximation by positive operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 3 , December 1982 , pp. 364 - 373
Copyright
Copyright © Australian Mathematical Society 1982

References

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