STABILITY RESULTS FOR CONVERGENCE OF CONVEX SETS AND FUNCTIONS IN NONREFLEXIVE SPACES

被引：2
作者：
Lahrache, J. [1 ]
机构：
[1] Univ C Doukkali, Fac Sci Math, El Jadida 24000, Morocco
来源：
PUBLICACIONS MATEMATIQUES | 1996年 / 40卷 / 01期
关键词：
Convex function; infconvolution; episum; epigraphical difference; slice topology; Mosco-convergence; bounded Hausdorff topology;
D O I：
10.5565/PUBLMAT_40196_05
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Gamma(X) be the convex proper lower semicontinuous functions on a normed linear space X. We show, subject to Rockafellar's constraints qualifications, that the operations of sum, episum and restriction are continuous with respect to the slice topology that reduces to the topology of Mosco convergence for reflexive X. We show also when X is complete that the epigraphical difference is continuous. These results are applied to convergence of convex sets.
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页码：67 / 83
页数：17
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