This paper deals with a new concept of limit for sequences of locally compact vector-valued mappings in normed spaces. We generalize the well-known concept of Γ-convergence to the so-called ΓΛ,μ - convergence in vector-valued case. To this aim, we study the link between the lower semicontinuity property of vector-valued mappings and the topological properties of their coepigraphs. We show that, if the objective space is partially ordered by a pointed cone with nonempty interior, then coepigraphs are stable with respect to their closure and, moreover, the locally semicompact vector-valued mappings with closed coepigraphs are lower continuous. Using these results, we establish the relationship between ΓΛ,μ -convergence of the sequences of mappings and K-convergence of their coepigraphs in the sense of Kuratowski and study the main topological properties of ΓΛ,μ -limits.

On the Concept of Γ-Convergence for Locally Compact Vector-Valued Mappings

MANZO, Rosanna
2011

Abstract

This paper deals with a new concept of limit for sequences of locally compact vector-valued mappings in normed spaces. We generalize the well-known concept of Γ-convergence to the so-called ΓΛ,μ - convergence in vector-valued case. To this aim, we study the link between the lower semicontinuity property of vector-valued mappings and the topological properties of their coepigraphs. We show that, if the objective space is partially ordered by a pointed cone with nonempty interior, then coepigraphs are stable with respect to their closure and, moreover, the locally semicompact vector-valued mappings with closed coepigraphs are lower continuous. Using these results, we establish the relationship between ΓΛ,μ -convergence of the sequences of mappings and K-convergence of their coepigraphs in the sense of Kuratowski and study the main topological properties of ΓΛ,μ -limits.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/3037049
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact