From Hahn-Banach to Monotonicity
Publication year: 2008
: 978-1-4020-6919-2
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.
: Mathematics and Statistics, Hahn-Banach-Lagrange theorem, Lagrange multipliers, convex analysis, functional analysis, monotone multifunctions, topologies on the bidual of a Banach space
