Minimax and Monotonicity
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1693
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1693
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Stephen Simons
Minimax and Monotonicity
Springer
Author Stephen Simons Department of Mathematics University of California Santa Barbara CA 93106-3080, USA [email protected]
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Die Deutsche Bibliothek • CIP-Einheitsaufnahme
Simons. Stephen: Minimax and monotonicity / Stephen Simons. - Berlin; Heidelberg. New York; London; Paris; Tokyo; Hong Kong; Barcelona; Budapest. Springer, 1998 (Lecture notes in mathematics; 1693) ISBN 3-540-64755-4
Mathematics Subject Classification (1991): 47H05, 47H04, 46BlO, 49135, 47NlO ISSN 0075-8434 ISBN 3-540-64755-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Printed in Germany
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For Tacoueiine
Preface
These notes had their genesis in three hours of lectures that were given in a "School" on minimax theorems that was held in Erice, Sicily in September - October, 1996. This was followed by an expanded version in five hours of lectures at the "Spring School" on Banach spaces in Paseky in the Czech Republic in April, 1997 which was followed, in turn, by an even more expanded version in ten hours of lectures at the University of Toulouse, France in May - June, 1997. The lectures were initially conceived as three isolated applications of minimax theorems to the theory of monotone multi functions. With each successive iteration, the emphasis gradually shifted to an examination of the "minimax technique" , a method for proving the existence of continuous linear functionals on a Banach space, and to the relationship between this technique and monotone multifunctions, To this was finally added an attempt to collect together the results that have been proved on monotone and maximal monotone multifunctions on Banach spaces in recent years, and organize them into a coherent theory. I would like to thank many people for their help and encouragement during the various stages of this project. I would first like to thank Biagio Ricceri for inviting me to Erice, Jaroslav Lukes, Jiri Kottas and Vac1av Zizler for inviting me to Paseky, and Jean-Baptiste Hiriart-Urruty for inviting me to Toulouse. I appreciate n
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