On -convergence of vector-valued mappings
Rosanna Manzo · 2014
This paper deals with a new concept of limit for sequences of vector-valued mappings in normed spaces. We generalize the well-known concept of � -convergence tothecaseofvector-valued mappingsandspecifynotionof � �,μ -convergence similar to the one previously introduced in Dovzhenko et al. (Far East J Appl Math 60:1-39, 2011). In particular, we show that � �,μ -convergence concept introduced in this paper possesses a compactness property whereas this property was failed in Dovzhenko et al. (Far East J Appl Math 60:1-39, 2011). In spite of the fact this paper contains another definition of � �,μ -limits for vector-valued mapping we prove that the � �,μ - lower limit in the new version coincides with the previous one, whereas the � �,μ - upper limit leads to a different mapping in general. Using the link between the lower semicontinuity property of vector-valued mappings and the topological properties of their coepigraphs, we establish the connection between � �,μ -convergence of the sequences of mappings and K-convergence of their epigraphs and coepigraphs in the sense of Kuratowski and study the main topological properties of � �,μ -limits. The