On the maximality of sums of nonlinear monotone operators
On the maximality of sums of nonlinear monotone operators
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DOI：
10.1090/s0002-9947-1970-0282272-5
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发表时间：
1970
影响因子：
1.3
通讯作者：
R. Rockafellar
中科院分区：
文献类型：
--
作者：
R. Rockafellar
（15）（T1 + T2）（x）= Tx（x）+ T2（x）= {*？+x% I xf e Tx（x），xt e T2（x）}。然而，如果Tx和F2是最大的，则不一定遵循F1 + T2是最大的-需要某种条件，因为例如Tx + T2的图甚至可以是空的（如当D（Tx）n D（T2）= 0时发生的）。确定Tx + T2是最大的条件的问题在单调算子理论中具有根本的重要性。Lescarret [9]和Browder [5]，[6]，[7]证明了这方面的结果。目前已知的最强结果是：
(1 5) (Ti + T2)(x) = Tx(x) + T2(x) = {*? +x% I xf e Tx(x), xt e T2(x)}. If Tx and F2 are maximal, it does not necessarily follow, however, that F», + T2 is maximal—some sort of condition is needed, since for example the graph of Tx + T2 can even be empty (as happens when D(Tx) n D(T2)= 0). The problem of determining conditions under which Tx + T2 is maximal turns out to be of fundamental importance in the theory of monotone operators. Results in this direction have been proved by Lescarret [9] and Browder [5], [6], [7]. The strongest result which is known at present is :