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

Publicacions Matemàtiques (1996)

- Volume: 40, Issue: 1, page 67-83
- ISSN: 0214-1493

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topLahrache, Jaafar. "Stability results for convergence of convex sets and functions in nonreflexive spaces.." Publicacions Matemàtiques 40.1 (1996): 67-83. <http://eudml.org/doc/41253>.

@article{Lahrache1996,

abstract = {Let Γ(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.},

author = {Lahrache, Jaafar},

journal = {Publicacions Matemàtiques},

keywords = {Funciones convexas; Espacios normados; Teoremas de convergencia; infconvolution; bounded Hausdorff topology; lower semicontinuous functions; episum; slice topology; Mosco convergence; epigraphical difference; convergence of convex sets},

language = {eng},

number = {1},

pages = {67-83},

title = {Stability results for convergence of convex sets and functions in nonreflexive spaces.},

url = {http://eudml.org/doc/41253},

volume = {40},

year = {1996},

}

TY - JOUR

AU - Lahrache, Jaafar

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

JO - Publicacions Matemàtiques

PY - 1996

VL - 40

IS - 1

SP - 67

EP - 83

AB - Let Γ(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.

LA - eng

KW - Funciones convexas; Espacios normados; Teoremas de convergencia; infconvolution; bounded Hausdorff topology; lower semicontinuous functions; episum; slice topology; Mosco convergence; epigraphical difference; convergence of convex sets

UR - http://eudml.org/doc/41253

ER -

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