Integration by parts for some general integrals

Author:

Das U.,Das A.G.

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference19 articles.

1. A Banach space of functions of generalized variation

2. On absolutely kth continuous functions

3. Convergence in kth variation and RSk integrals

4. A new characterisation of k-fold Legesgue integral;Das;Comment. Math. Prace Mat.,1988

5. On functions of bounded essential kth variation;De Sarkar;Bull. Calcutta Math. Soc.,1986

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