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An Extension of M. Riesz's Mean Value Theorem for Infinite Integrals

Published online by Cambridge University Press:  20 November 2018

B. Choudhary  and
Ashok Kumar
B. Choudhary
Affiliation:
Indian Institute of Technology, Hauz Khas, New Delhi, India
Ashok Kumar
Affiliation:
Indian Institute of Technology, Hauz Khas, New Delhi, India
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Isaacs [4] has proved the following theorem.

Theorem A. If 0 < α < 1 and

is convergent, then for u < w,

1.1

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 1016 - 1024
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bosanquet, L. S., Some extensions of M. Riesz's mean value theorem, Indian J. Math. 9 (1967), 65–90.Google Scholar
2. Bosanquet, L. S., A functional equation related to Rieszs mean value theorem, Publ. Ramanujan Inst. 1 (1969), 47–69.Google Scholar
3. Choudhary, B., An extension of Abel's integral equation, J. Math. Anal. Appl. 44 (1973), 113–130.Google Scholar
4. Isaacs, G. L., M. Riesz's mean value theorem for infinite integrals, J. London Math. Soc. 28 (1953), 171–176.Google Scholar