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On a Class of Positive Linear Operators

Published online by Cambridge University Press:  20 November 2018

J. Swetits  and
B. Wood
J. Swetits
Affiliation:
Old Dominion University, Norfolk, Virginia
B. Wood
Affiliation:
University of Arizona, Tucson, Arizona
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In a recent paper [3] Meir and Sharma introduced a generalization of the Sα- method of summability. The elements of their matrix, (ank), are defined by

(1)

where is a sequence of complex numbers. if 0 < αj < l for each j = 0, 1, 2,… then ank≥0 for each n = 0, 1, 2,… and k = 0,1,2,…

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 557 - 559
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Baskakov, V. A., An example of a sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR, 113 (1957), 249–251.Google Scholar
2. King, J. P., The Lototsky transform and Bernstein polynomials, Canad. J. Math. 18 (1966), 89–91.Google Scholar
3. Meir, A. and Sharma, A., A generalization of the Sα summation method, Proc. Cambridge Philos. Soc. 67 (1970), 61–66.Google Scholar
4. Pethe, S., Some two point expansions and related classes of functions, Ph.Dissertation, D., Univ. of Calgary, (1971), 91–95.Google Scholar