Convergence in kth variation and RSk integrals

Author:

Das U.,Das A. G.

Abstract

AbstractIn recent papers, Russell introduced the notions of functions of bounded kth variation (BVk functions) and the RSk integral. Das and Lahiri enriched Russell's works along with a convergence formula of RSk integrals depending on the convergence of integrands. In this paper a convergence theorem analogous to Arzela's dominated convergence theorem has been presented. An investigation to the convergence in kth variation has been made leading to some convergence theorems of RSk integrals depending on the convergence of integrators.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference8 articles.

1. Stieltjes-type integrals

2. Arzela's dominated convergence theorem for the Riemann integral;Luxemburg;Amer. Math. Monthly,1971

3. On absolutely kth continuous functions

4. On RSk integrals;Das;Comment. Math. Univ. Carolinae,1980

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1. A generalized Henstock-Stieltjes integral involving division functions;Mathematica Slovaca;2008-06-14

2. Generalised Hölderian functions;Bulletin of the Australian Mathematical Society;1989-08

3. Integration by parts for some general integrals;Bulletin of the Australian Mathematical Society;1988-02

4. Riemann derivatives and general integrals;Bulletin of the Australian Mathematical Society;1987-04

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