Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-29T02:39:32.622Z Has data issue: false hasContentIssue false
  • English
  • Français

A Class of Positive Linear Operators

Published online by Cambridge University Press:  20 November 2018

J. P. King
J. P. King*
Affiliation:
Lehigh University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let F[a, b] be the linear space of all real valued functions defined on [a, b]. A linear operator L: C[a, b] → F[a, b] is called positive (and hence monotone) on C[a, b] if L(f)≥0 whenever f≥0. There has been a considerable amount of research concerned with the convergence of sequences of the form {Ln(f)} to f where {Ln} is a sequence of positive linear operators on C[a, b].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 51 - 59
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Cheney, E.W. and Sharma, A., Bernstein power series Can. J. Math., (1964)241-252.10.4153/CJM-1964-023-1Google Scholar
2. Jakimovski, A. and Leviatan, D., Generalised Bernstein polynomials, Math. Zeitschr. 93 (1966), 416-426.10.1007/BF01112029Google Scholar
3. Jakimovski, A. and Leviatan, D., Generalised Bernstein power series, Math. Zeitschr., 96 (1967), 333-342.10.1007/BF01117094Google Scholar
4. Korovkin, P.P., Linear operators and approximation theory (translated from the Russian edition of 1959), (Delhi, 1960).Google Scholar
5. Lorentz, G.G., Bernstein polynomials, Toronto, (1953).Google Scholar
6. Sonnenschein, J., Sur les séries divergentes, Bull.Acad. Roy. de Belg. Cl. Sci., 35 (1949), 594-601.Google Scholar
7. Szasz, O., Generalizations of S. Bernstein's polynomials to the infinite interval, J. Res. Nat. Bur. Standards Sect. B, 45 (1950), 239-245.10.6028/jres.045.024Google Scholar