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On Generalized Averaging Operators

Published online by Cambridge University Press:  20 November 2018

R. P. Boas
R. P. Boas*
Affiliation:
Northwestern University Evanston, Illinois
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Let Sumner (4) has discussed for arbitrary real λ and h, whereƒ(Z) is an entire function of exponential type I shall show that in this case an alternative definition of ∇λλ, which leads to Sumner's results more quickly, is equivalent to Sumner's. (However, Sumner's definition is, in principle, applicable to a wider class of functions.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 122 - 126
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Boas, R. P., Jr., Entire functions (New York, 1954).Google Scholar
2. Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
3. Sheffer, I. M., Some applications of certain polynomial classes, Bull. Amer. Math. Soc, 47 (1941), 885–898.Google Scholar
4. Sumner, D. B., A generalized averaging operator, Can. J. Math., 8 (1956), 437-446.Google Scholar