Affordable Access

Parametrization of Carathéodory multifunctions

Authors
Publication Date
Disciplines
  • Law

Abstract

Parametrization of Carathéodory multifunctions RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA ANTÓNIOORNELAS Parametrization of Carathéodorymultifunctions Rendiconti del Seminario Matematico della Università di Padova, tome 83 (1990), p. 33-44. <http://www.numdam.org/item?id=RSMUP_1990__83__33_0> © Rendiconti del Seminario Matematico della Università di Padova, 1990, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Parametrization of Carathéodory Multifunctions. ANTÓNIO ORNELAS (*) 1. Introduction. Let F: be a multifunction which is Lipschitz with con- stant I and has values bounded by m. We show that co can be represented as f (x, U), with U the unit closed ball in Rn and f Lipschitz with constant 6n(21 + m). Existing representations were: either with U the unit closed ball in Rn but f just continuous in (x, u) (Ekeland-Valadier [3]); or with f Lipschitz in (x, u) but U in some infinite dimensional space (LeDonne-Marchi [6]). More generally, let F: be a multifunction with .F’( ~ , x) measurable and .F(t, ~ ) uniformly continuous. We show that co F(t, x) can be represented as f (t, x, U), where U is either the unit closed ball in Rn (in case the values F(t, x) are compact) or U = Rn (in case the values F(t, x) are unbounded). As to f, we obtain f(., x, u) meas- urable and f (t, ~ , ~ ) uniformly continuous (with modulus of con- tinuity equal to that of F(t, ·) multiplied by a constant). A consequence of this is that differential inclus

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Sandwich-type theorem for Carathéodory multifuncti...

on Journal of Mathematical Analys... Jan 01, 2008

Carathéodory sequence parametrizations of Potapov-...

on Linear Algebra and its Applica... Jan 01, 1995

On multifunctions

Jan 01, 2001
More articles like this..