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A simple proof of the sum formula

Published online by Cambridge University Press:  17 April 2009

A. Verona  and
M. E. Verona
A. Verona
Affiliation:
Department of Mathematics and Computer Science, California State University, Los Angeles, CA 90032, United States of America, e-mail: averona@calstatela.edu
M. E. Verona
Affiliation:
Department of Mathematics, DRB 155, University of Southern California, Los Angeles, CA 90089–1113, Untied States of America, e-mail: Verona@math.use.edu
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Abstract

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In this note we present a simple, short proof of the sum formula for subdifferentials of convex functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 337 - 339
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Attouch, H. and Brezis, H., ‘Duality for the sum of convex functions in general Banach spaces’, in Aspects of Mathematics and its Applications, (Barroso, J.A., Editor), North Holland Math. Library 34 (North-Holland, Amsterdam, New York, 1986), pp. 125–133.CrossRefGoogle Scholar
[2]Phelps, R.R., Convex functions, monotone operators and differentiability (2nd Edition), Lecture Notes in Mathematics 1364 (Springer-Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar
[3]Simons, S., ‘Sum theorems for monotone operators and convex functions’, Trans. Amer. Math. Soc. 350 (1998), 2953–2972.CrossRefGoogle Scholar