Sum Theorems for Monotone Operators and Convex Functions Export

@article{citeulike:2388516, abstract = {In this paper, we derive sufficient conditions for the sum of two or more maximal monotone operators on a reflexive Banach space to be maximal monotone, and we achieve this without any renorming theorems or fixed-point-related concepts. In the course of this, we will develop a generalization of the uniform boundedness theorem for (possibly nonreflexive) 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 to obtain additional results on the relation between the effective domains of such functions and the domains of their sub-differentials. The other main tool that we use is a standard minimax theorem.}, author = {Simons, S.}, citeulike-article-id = {2388516}, citeulike-linkout-0 = {http://www.jstor.org/stable/117738}, journal = {Transactions of the American Mathematical Society}, keywords = {convexity, fenchel\_duality, minimax}, number = {7}, pages = {2953--2972}, posted-at = {2008-02-16 12:57:09}, priority = {3}, title = {Sum Theorems for Monotone Operators and Convex Functions}, url = {http://www.jstor.org/stable/117738}, volume = {350}, year = {1998} }

TY - JOUR ID - citeulike:2388516 L3 - citeulike-article-id:2388516 N2 - In this paper, we derive sufficient conditions for the sum of two or more maximal monotone operators on a reflexive Banach space to be maximal monotone, and we achieve this without any renorming theorems or fixed-point-related concepts. In the course of this, we will develop a generalization of the uniform boundedness theorem for (possibly nonreflexive) 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 to obtain additional results on the relation between the effective domains of such functions and the domains of their sub-differentials. The other main tool that we use is a standard minimax theorem. IS - 7 JF - Transactions of the American Mathematical Society EP - 2972 TI - Sum Theorems for Monotone Operators and Convex Functions VL - 350 SP - 2953 KW - convexity KW - fenchel_duality KW - minimax AU - Simons, S PY - 1998/// UR - http://www.jstor.org/stable/117738 ER -