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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A limiting example
for the Local ``fuzzy'' sum rule
in nonsmooth analysis


Authors: Jon Vanderwerff and Qiji J. Zhu
Journal: Proc. Amer. Math. Soc. 126 (1998), 2691-2697
MSC (1991): Primary 26B05, 49J50, 49J52
MathSciNet review: 1451834
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that assuming all the summand functions to be lower semicontinuous is not sufficient to ensure a (strong) fuzzy sum rule for subdifferentials in any infinite dimensional Banach space. From this we deduce that additional assumptions are also needed on functions for chain rules, multiplier rules for constrained minimization problems and Clarke-Ledyaev type mean value inequalities in the infinite dimensional setting.


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Additional Information

Jon Vanderwerff
Affiliation: Department of Mathematics, Walla Walla College, College Place, Washington 99324
Email: vandjo@wwc.edu

Qiji J. Zhu
Affiliation: Department of Mathematics & Statistics, Western Michigan University, Kalamazoo, Michigan 49008
Email: zhu@math-stat.wmich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04365-2
PII: S 0002-9939(98)04365-2
Received by editor(s): January 30, 1997
Additional Notes: The first author’s research was partially supported by a Walla Walla College Faculty Development Grant.
The second author’s work was partially supported by a grant from the Faculty Research and Creative Activities Support Fund, Western Michigan University.
Research for this note was completed while the authors were visiting Simon Fraser University. The authors thank J.M. Borwein and the CECM for their hospitality.
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society