Author/Authors :
Niknam، A. نويسنده Department of Pure Mathematic, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran Niknam, A. , Shamsi Gamchi، S. نويسنده Department of Pure Mathematic, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran Shamsi Gamchi, S. , Janfada، M. نويسنده ,
Abstract :
In this paper we introduce the cone bounded linear mapping
and 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 TVS-cone norms are equivalent if and only if they induce equivalent
topologies. In the sequel, the notion of algebraic cone metric is introduced
and it is shown that every algebraic cone metric space has a topology and
the Banach fixed point theorem for contraction mappings on algebraic
cone metric spaces is proved.
