Stability results for convergence of convex sets and functions in nonreflexive spaces

Autores: J. Lahrache
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 40, Nº 1, 1996, págs. 67-83
Idioma: inglés
DOI: 10.5565/publmat_40196_05
Títulos paralelos:
- Resultados de estabilidad para la convergencia de funciones y conjuntos convexos en espacios no reflexivos
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Resumen
- 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.