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
2011-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
