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

Lahrache, 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 -