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The SCnP-Integral and the Pn+1-Integral

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen  and
C. M. Lee
P. S. Bullen
Affiliation:
University of British Columbia, Vancouver, British Columbia;
C. M. Lee
Affiliation:
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
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In [2], we have briefly described, as examples of the general theory developed there, a scale of symmetric Cesaro-Perron integrals, namely SCnP-integral for n = 1, 2, 3, … . The purpose of this paper is to consider the integrals in a greater detail.

As a preliminary, we prove some lemmas, which are also interesting for their own sake, concerning the de la Vallée Poussin derivatives in Section 1, and we also state two deep theorems concerning the n-convex functions in Section 2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1274 - 1284
Copyright
Copyright © Canadian Mathematical Society 1973

References

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