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A New Approximation Operator Generalizing Meyer-König and Zellers Power Series

Published online by Cambridge University Press:  20 November 2018

Benny Levikson
Benny Levikson*
Affiliation:
Purdue University, West Lafayette, Indiana
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In this paper we introduce a new approximation operator of the Arato-Renyi type and study its properties. Special cases of our operator are the power-series, of W. Meyer-König and K. Zeller (see [9]) and the generalized Berenstein power series introduced by A. Jakimovski and D. Leviatan in [5] and analyzed by them in [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 301 - 311
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Arato, M. and Renyi, A., Probablistic proof of a theorem on the approximation of continuous functions by means of generalized Bernstein polynomials, Acta Math. Acad. Sci. Hungar 8 (1957), 91–97.Google Scholar
2. Ditzian, Z. and Jakimovski, A., Inversion and jump formulae for variation diminishing transforms, Annali di Mathematica pure et applicate 81, (1969), 261–318.Google Scholar
3. Hausdorff, F., Summationsmethoden und momentfolgen II, Math Zeit. 9 (1921), 280–299.Google Scholar
4. Jakimovski, A., Generalized Bernstein polynomials for discontinuous and convex functions, J. d'anal. Math. 23 (1970), 171–183.Google Scholar
5. Jakimovski, A. and Leviatan, D., A property of approximation operators and application to Tauberian constants, Math. Zeit. 102 (1967), 177–204.Google Scholar
6. Jakimovski, A. and Leviatan, D., Completeness and approximation operators, Publ. Ramanujan Inst. (Madras) 1 (1969), 123–129.Google Scholar
7. Leviatan, D., On approximation operators of the Berenstein type, J. Approximation Theory 1 (1968), 275–278.Google Scholar
8. Loeve, M., Probability theory (D. Van-Nostrand Company, Princeton, N.J. 3rd Edition, 1970).Google Scholar
9. Meyer-Kônig, W. and Zeller, K., Berensteinsche Potenzreichen, Studia Mathematica 19 (1960), 89–94.Google Scholar
10. Renyi, A., Foundations of probability (Holden-Day, Inc. San Francisco, 1970).Google Scholar