SUM THEOREMS FOR MONOTONE-OPERATORS AND CONVEX-FUNCTIONS

In this paper, we derive sufficient conditions for the sum of two or m ore maximal monotone operators on a reflexive Banach space to be maxim al monotone, and we achieve this without any renorming theorems or fix ed-point-related concepts. In the course of this, we will develop a ge neralization of the uniform boundedness theorem for (possibly nonrefle xive) Banach spaces. We will apply this to obtain the Fenchel Duality Theorem for the sum of two or more proper, convex lower semicontinuous functions under the appropriate constraint qualifications, and also t o obtain additional results on the relation between the effective doma ins of such functions and the domains of their subdifferentials. The o ther main tool that we use is a standard minimax theorem.