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Approximation of Functions by a Bernstein-Type Operator

Published online by Cambridge University Press:  20 November 2018

S. P. Pethe  and
G. C. Jain
S. P. Pethe
Affiliation:
University of Calgary, Calgary, Alberta
G. C. Jain
Affiliation:
University of Calgary, Calgary, Alberta
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Various generalizations of the Bernstein operator, defined on C[0, 1] by the relation

1.1

where

have been given. Note that bnk(x) is the well-known binomial distribution.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 551 - 557
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Cheney, E. W., and Sharma, A., On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma (2) 5 (1964), 77-82.Google Scholar
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3. Meyer-König, W., and Zeller, K., Bernsteinsche Potenzreihen, Studia Math. 19 (1960), 89-94.Google Scholar
4. Patil, G. P., and Joshi, S. W., A dictionary and bibliography of discrete distributions, Oliver and Boyd, Edinburgh, 1968.Google Scholar
5. Stancu, D. D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl., (XIII) 8 (1968), 1173-1194.Google Scholar