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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
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Abstract

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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