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Integration by parts for some general integrals

Published online by Cambridge University Press:  17 April 2009

U. Das  and
A.G. Das
U. Das
Affiliation:
Department of Mathematics, Faculty of Science, University of Kalyani, West Bengal 741235, India
A.G. Das
Affiliation:
Department of Mathematics, Faculty of Science, University of Kalyani, West Bengal 741235, India
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Abstract

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The present work is concerned with an integration by parts formula for the Pk-integral of De Sarkar and Das, and of the equivalent Pk-integral of Bullen. The process involves a simpler and updated version of that for the Zk−1-integral of Bergin. If f is Pk – (Zk−1)-integrable and G is of bounded kth variation, then fG is Pk – (Zk−1)-integrable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 1 - 15
Copyright
Copyright © Australian Mathematical Society 1988

References

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