Journal of Convex Analysis 32 (2025), No. 3, 661--680
Copyright Heldermann Verlag 2025
Convergence of Slopes in Asplund Spaces
Pedro Pérez-Aros
Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile
pperez@dim.uchile.cl
Lionel Thibault
Institut Montpelliérain A. Grothendieck, Université de Montpellier, France
lionel.thibault@umontpellier.fr
Dariusz Zagrodny
Faculty of Mathematics and Computer Science, University of Lodz, Poland
dariusz.zagrodny@wmii.uni.lodz.pl
We investigate the epigraphical convergence of slopes of lower semicontinuous convex functions on Asplund spaces. This type of convergence of slopes is compared to the Painlevé-Kuratowski convergence of subdifferentials. Both convergences are shown to be equivalent under mild conditions of compactness type.
Keywords: Convex function, slope, convergence of slopes, subdifferential, convergence of subdifferentials.
MSC: 49J52; 47J22, 58E30.
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