Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-26T14:51:35.345Z Has data issue: false hasContentIssue false
  • English
  • Français

New directions in convex analysis: the differentiability of convex functions on topological linear spaces

Published online by Cambridge University Press:  17 April 2009

Bernice Sharp
Bernice Sharp
Affiliation:
Catholic College of Education, Sydney40 Edward StNorth Sydney NSW 2060Australia
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian Ph.D. theses
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 333 - 335
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Asplund, E., ‘Fréchet differentiability of convex functions’, Acta Math 121 (1968), 31–47.CrossRefGoogle Scholar
[2]Averbukh, V.I. and Smolyanov, O.G., ‘The theory of differentiation in linear topological spaces’, Russian Math. Surveys 22 6 (1967), 201–258.CrossRefGoogle Scholar
[3]Averbukh, V.I. and Smolyanov, O.G., ‘The various definitions of the derivative in linear topological spaces’, Russian Math. Surveys 23 4 (1968), 67–113.CrossRefGoogle Scholar
[4]Borwein, J.M., ‘Continuity and differentiability properties of convex operators’, Proc. London Math. Soc. 3 (1982), 420–444.CrossRefGoogle Scholar
[5]Borwein, J.M., ‘Generic differentiability of order-bounded convex operators’, J. Austral. Math. Soc. Ser. B 28 (1986), 22–29.CrossRefGoogle Scholar
[6]Čoban, M. and Kenderov, P., ‘Dense Gateaux differentiability of the sup-norm in C(T) and the topological properties of T’, C.R.Acad. Bulgare Sci. 38 (1985), 1603–1604.Google Scholar
[7]Giles, J.R., Convex analysis with application in differentiation of convex functions (Research Notes in Mathematics 58 Pitman, 1982).Google Scholar
[8]Larman, D.G. and Phelps, R., ‘Gateaux differentiabilty of convex functions on Banach spaces’, J. London Math. Soc (2) 20 (1979), 115–127.CrossRefGoogle Scholar
[9]Mazur, S., ‘Über konvexe Mengen in linearen normierten Räumen’, Studia Math 4 (1933), 70–84.CrossRefGoogle Scholar
[10]Namioka, and Phelps, R., ‘Banach spaces which are Asplund spaces’, Duke Math. J. 42 (1975), 735–750.CrossRefGoogle Scholar
[11]Phelps, R., Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics 1364, Springer-Verlag, 1989).CrossRefGoogle Scholar