Hostname: page-component-54dcc4c588-5q6g5 Total loading time: 0 Render date: 2025-09-20T15:02:47.249Z Has data issue: false hasContentIssue false
  • English
  • Français

A Continuity-Like Property of Derivatives

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen  and
D. N. Sarkhel
P. S. Bullen
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, e-mail: bullen@math.ubc.ca
D. N. Sarkhel
Affiliation:
Department of Mathematics, University of Kalyani, Kalyani, W.B., India 741235
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.

In this paper a refinement of property Z of Zahorski-Weil is defined and shown to be, like the weaker property Z, satisfied by all common derivatives.

Keywords

26A24Derivativeapproximate derivativePeano derivativeapproximate Peano derivativeproperty Z

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 10 - 20
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Babcock, B. S., On properties of the approximate Peano derivatives, Trans. Amer. Math. Soc. 212(1975), 274–294.Google Scholar
2. Clarkson, J. A., A property of derivatives, Bull. Amer. Math. Soc. 53(1947), 124–125.Google Scholar
3. Denjoy, A., Sur une propriété des fonctions dérivées exactes, Enseignement Math. 18(1916), 320–328.Google Scholar
4. Denjoy, A., Sur l'intégration des coefficients différentiels d'ordre supérieur, Fund. Math. 25(1935), 273–326.Google Scholar
5. Evans, M. J., Lp derivatives and approximate Peano derivatives, Trans. Amer. Math. Soc. 165(1972), 381– 388.Google Scholar
6. Goffinan, C. and Neugebauer, C. J., On approximate derivatives, Proc. Amer. Math. Soc. 11(1960), 962– 966.Google Scholar
7. Khintchine, A., Recherches sur la structure des fonctions mesurables, Fund. Math. 9(1927), 217—279.Google Scholar
8. Mafik, J., On generalized derivatives, Real Anal. Exchange 3(1977-1978), 87–92.Google Scholar
9. Marcus, S., On a theorem of Denjoy and on approximate derivative, Monatsh. Math. 66(1962), 435–440.Google Scholar
10. Mukhopadhyay, S. N., On the approximate Peano derivatives, Fund. Math. 88(1975), 133–143.Google Scholar
11. Neugebauer, C. J., Darboux functions of Baire class one and derivatives, Proc. Amer. Math. Soc. 13( 1962), 838–843.Google Scholar
12. Oliver, H. W., The exact Peano derivatives, Trans. Amer. Math. Soc. 76(1954), 444–456.Google Scholar
13. Saks, S., Theory of the Integral, Dover, New York, 1964.Google Scholar
14. Sarkhel, D. N., Thepointwise characterization of derivatives of integrals, Proc. Amer. Math. Soc. 63(1977), 125–128.Google Scholar
15. Tolstoff, G. P., Sur la dérivée approximative exacte, Rec. Math. (Mat. Sb.), (N.S.) 4(1938), 499–504.Google Scholar
16. Weil, C. E., On properties of derivatives, Trans. Amer. Math. Soc. 114(1965), 363—376.Google Scholar
17. Weil, C. E., A property for certain derivatives, Indiana Univ. Math. J. 23(1973/74), 527—536.Google Scholar
18. Zahorski, Z., Sur la première dérivée, Trans. Amer. Math. Soc. 69(1950), 1—54.Google Scholar