Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T17:20:54.439Z Has data issue: false hasContentIssue false
  • English
  • Français

Functions of bounded kth variation and absolutely kth continuous functions

Published online by Cambridge University Press:  17 April 2009

S.K. Mukhopadhyay  and
S.N. Mukhopadhyay
S.K. Mukhopadhyay
Affiliation:
Department of Mathematics, The University of Burdwan Burdwan–713104, West Bengal, India
S.N. Mukhopadhyay
Affiliation:
Department of Mathematics, The University of Burdwan Burdwan–713104, West Bengal, India
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Functions of bounded kth variation and absolutely kth continuous functions are considered on sets and various properties are studied.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 91 - 106
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bullen, P.S. and Mukhopadhyay, S.N., ‘Relations between some general nth order derivatives’, Fund. Math. 85 (1974), 257–276.CrossRefGoogle Scholar
[2]Das, A.G. and Lahiri, B.K., ‘On absolutely kth continuous functions’, Fund. Math. 105 (1980), 159–169.CrossRefGoogle Scholar
[3]Deb, T.K. and De Sarkar, S., ‘On points of kth absolute continuity’, J. Indian Inst. Sci. 66 (1986), 457–464.Google Scholar
[4]Denjoy, A., ‘Sur l' integration des coefficients differentiels 'ordre Superieur’, Fund. Math. 25 (1935), 273–326.CrossRefGoogle Scholar
[5]De Sarkar, S. and Das, A.G., ‘On functions of bounded kth variation’, J. Indian Inst. Sci. 64 (1983), 299–309.Google Scholar
[6]Mukhopadhyay, S.N. and Sain, D.N., ‘On functions of bounded nth variation’, Fund. Math. 131 (1988), 191–208.CrossRefGoogle Scholar
[7]Russell, A.M., ‘Functions of bounded kth variation’, Proc. London Math. Soc. 26 (1973), 547–563.CrossRefGoogle Scholar
[8]Sain, D.N. and Mukhopadhyay, S.N., ‘Characterizations of absolutely nth continuous function and of function of bounded nth variation’, (submitted).Google Scholar
[9]Saks, S., Theory of integrals (Dover, 1937).Google Scholar
[10]Sarkhel, D.N., ‘A new approach to kth variation’, Indian J. Math. 32 (1990), 135–169.Google Scholar