ON THE MAXIMALITY OF SUMS OF NONLINEAR MONOTONE OPERATORS

ON THE MAXIMALITY OF SUMS OF NONLINEAR MONOTONE OPERATORS

May 1970 | R. T. ROCKAFELLAR
This paper investigates the maximality of sums of nonlinear monotone operators in a real Banach space. The main result establishes that under certain conditions, the sum of two maximal monotone operators is also maximal. Specifically, if the domains of the operators intersect in the interior or if one operator is locally bounded at a point in the closure of the intersection of their domains, then their sum is maximal. The result is proven using properties of monotone operators, duality mappings, and related theorems. The paper also discusses applications to variational inequalities and provides conditions under which the sum of two monotone operators is maximal. The results are supported by various theorems and lemmas, including a generalization of Minty's theorem and a result on the local boundedness of monotone operators. The paper concludes with applications to variational inequalities and a corollary related to the existence of solutions under certain constraints.This paper investigates the maximality of sums of nonlinear monotone operators in a real Banach space. The main result establishes that under certain conditions, the sum of two maximal monotone operators is also maximal. Specifically, if the domains of the operators intersect in the interior or if one operator is locally bounded at a point in the closure of the intersection of their domains, then their sum is maximal. The result is proven using properties of monotone operators, duality mappings, and related theorems. The paper also discusses applications to variational inequalities and provides conditions under which the sum of two monotone operators is maximal. The results are supported by various theorems and lemmas, including a generalization of Minty's theorem and a result on the local boundedness of monotone operators. The paper concludes with applications to variational inequalities and a corollary related to the existence of solutions under certain constraints.
Reach us at info@futurestudyspace.com
[slides and audio] On the maximality of sums of nonlinear monotone operators