Generalized Convexity and Related Topics
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Igor V. Konnov · Dinh The Luc · Alexander M. Rubinov†
Generalized Convexity and Related Topics With 11 Figures
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Professor Igor V. Konnov Department of Applied Mathematics Kazan University ul. Kremlevskaya, 18 Kazan 420008 Russia [email protected] Professor Dinh The Luc Department de Mathematiques 33 rue Louis Pasteur 84000 Avignon France [email protected] Professor Alexander M. Rubinov† SITMS University of Ballarat University Dr. 1 3353 Victoria Australia [email protected]
Library of Congress Control Number: 2006934206
ISBN-10 3-540-37006-4 Springer Berlin Heidelberg New York ISBN-13 978-3-540-37006-2 Springer 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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 is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by author Cover: Erich Kirchner, Heidelberg Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig SPIN 11811275
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Preface
In mathematics generalization is one of the main activities of researchers. It opens up new theoretical horizons and broadens the fields of applications. Intensive study of generalized convex objects began about three decades ago when the theory of convex analysis nearly reached its perfect stage of development with the pioneering contributions of Fenchel, Moreau, Rockafellar and others. The involvement of a number of scholars in the study of generalized convex functions and generalized monotone operators in recent years is due to the quest for more general techniques that are able to describe and treat models of the real world in which convexity and monotonicity are relaxed. Ideas and methods of generalized convexity are now within reach not only in mathematics, but also in economics, engineering, mechanics, finance and other applied sciences. This volume of referred papers, carefully selected from the contributions delivered at the 8th International Symposium on Generalized Convexity and Monotonicity (Varese, 4-8 July, 2005), offers a global picture of current trends of research in generalized convexity and generalized monotonicity. It begins with three invited lectures by Konnov, Levin and Pardalos on numerical variation
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