In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space.
The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1693 Stephen Simons From Hahn-Banach to Monotonicity 2nd, expanded edition ABC Stephen Simons Department of Mathematics University of California Santa Barbara, CA 93105-3080 USA
[email protected] http://www.math.ucsb.edu/∼simons 1st edition 1998 LNM 1693: Minimax and Monotonicity ISBN 978-1-4020-6918-5 e-ISBN 978-1-4020-6919-2 DOI 10.1007/978-1-4020-6919-2 Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2007942159 Mathematics Subject Classification (2000): 46A22, 49J35, 47N10, 49