On the inner and outer norms of sublinear mappings

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Title: On the inner and outer norms of sublinear mappings
Authors: Aragón Artacho, Francisco Javier | Dontchev, Asen L.
Research Group/s: Programación Semi-infinita
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Mathematical Reviews
Keywords: Set-valued mapping | Convex graph | Sublinear mapping | Inner norm | Outer norm
Knowledge Area: Matemáticas
Issue Date: Mar-2007
Publisher: Springer Netherlands
Citation: ARAGÓN ARTACHO, Francisco Javier; DONTCHEV, Asen L. "On the inner and outer norms of sublinear mappings". Set-Valued Analysis. Vol. 15, No. 1 (March 2007). ISSN 0927-6947, pp. 61-65
Abstract: In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with dom F = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously.
Sponsor: Grant BES-2003-0188 from FPI Program of MEC (Spain).
URI: http://hdl.handle.net/10045/8058
ISSN: 0927-6947 (Print) | 1572-932X (Online)
DOI: 10.1007/s11228-006-0034-4
Language: eng
Type: info:eu-repo/semantics/article
Rights: The original publication is available at www.springerlink.com
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s11228-006-0034-4
Appears in Collections:INV - LOPT - Artículos de Revistas

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