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The proximally continuous integrals

Published online by Cambridge University Press:  09 April 2009

D. N. Sarkhel
Affiliation:
Department of Mathematics, University of Kalyani, Kalyani, West Bengal, India
A. K. De
Affiliation:
Department of Mathematics, University of Kalyani, Kalyani, West Bengal, India
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Abstract

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This paper introduces certain generalization of the notions of approximate limit, continuity and derivative and of absolute continuity, of real functions, leading to generalized integrals of Perron and Denjoy types comprising the AP-integral of Burkill (1931) and Sonouchi and Utagawa (1949) and the AD-integral of Kubota (1963), respectiely. The generalizations are all substantiated by appropriate examples.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1981

References

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