Semicontinuity of vector-valued mappings

Abstract

We first provide, for a given vector-valued mapping f, a lower semicontinuous (l.s.c.) regularization. Further, we present a new characterization of lower semicontinuity, from which we derive some other type of l.s.c. regularizations. A quasi-l.s.c. regularization is thereafter presented.

†Dedicated to Diethard Pallaschke in celebration to his 65th birthday.

Keywords:

• Vector-valued mapping
• Lower semicontinuous regularization

Keywords:

• Mathematics Subject Classifications 2000: 26E25
• 58C07
• 49J52

Acknowledgments

Research of the first author was supported by “Agence Universitaire de la Francophonie (AUF)”, Conseil Régional du Limousin and by the project MOD (Modélisation, Optimisation, Dynamique) of XLIM (UMR-CNRS 6172) and by the University of Limoges.

Notes

†Dedicated to Diethard Pallaschke in celebration to his 65th birthday.