CONVERGENCE OF CONVEX SETS AND OF SOLUTIONS OF VARIATIONAL INEQUALITIES
CONVERGENCE OF CONVEX SETS AND OF SOLUTIONS OF VARIATIONAL INEQUALITIES
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DOI：
10.1016/0001-8708(69)90009-7
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发表时间：
1969-01-01
影响因子：
1.7
通讯作者：
MOSCO, U
中科院分区：
文献类型：
--
作者：
MOSCO, U
The main object of this paper is to study convergence properties of solutions of variational inequalities such as u~ K:(Tu, v-uj> O for all v E K,(1) where T is a monotone hemicontinuous mapping from a real reflexive Banach space X to its dual X* and K is a non-empty closed convex subset of the domain of T, when T and K are subjected to a perturbation. We consider a sequence (T,) of monotone hemicontinuous mappings from X to X*, a sequence (K,) of closed convex subsets of X, K,, contained in the domain of T,, and for each n the variational inequality u,~ K,:(T, u,, vu,,)> O for all v E K,,(111) and we ask under what condition the solutions of (1,)“converge” to the solutions of (l), as T,“converges” to T and K,“converges” to K. Real parametrized perturbations T, and K, would require only minor changes.
