AU - Niknam, Assadollah
AU - Shamsi Gamchi, Saeedeh
AU - Janfada, Mohammad
TI - Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 9
VI - 1
IP - 1
4099 - http://ijmsi.ir/article-1-360-en.html
4100 - http://ijmsi.ir/article-1-360-en.pdf
SO - IJMSI 1
ABĀ - In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we introduce the notion of algebraically cone metric and we will show that every algebraically cone metric space has a topology.
CP - IRAN
IN - Department of Pure Mathematic, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-
LG - eng
PB - IJMSI
PG - 71
PT - Research paper
YR - 2014