On an equivalence of topological vector space valued cone metric spaces and metric spaces
Küçük Resim Yok
Tarih
2012
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
PERGAMON-ELSEVIER SCIENCE LTD
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied by Du (2010) [14] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper, we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable, prove a completion theorem, and also obtain some more results in topological vector space valued cone normed spaces. (C) 2011 Elsevier Ltd. All rights reserved.
Açıklama
Anahtar Kelimeler
TVS-cone metric space, Generalized TVS-cone metric space, Cone Banach spaces, Set-valued operators
Kaynak
APPLIED MATHEMATICS LETTERS
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
25
Sayı
3
