Introduction

These notes fall into three distinct parts. In Chapter I, we discuss the “Hahn– Banach–Lagrange theorem”, a new version of the Hahn–Banach theorem, which gives very efficient proofs of the main existence theorems in functional analysis, optimization theory, minimax theory and convex analysis. In Chapter II, we zero in on the applications to convex analysis. In the remaining five chapters, we show how the results of the first two chapters can be used to obtain a large number of results on monotone multifunctions, many of which have not yet appeared in print.