Metrizability of Topological Vector Space Valued Cone Metric Spaces
Abstract
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. This is applied by Du (2010) [A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis 72 2259-2261] 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.
Keywords
Cite
@article{arxiv.1007.3123,
title = {Metrizability of Topological Vector Space Valued Cone Metric Spaces},
author = {Huseyin Cakalli and Ayse Sonmez and Cigdem Genc},
journal= {arXiv preprint arXiv:1007.3123},
year = {2011}
}
Comments
This paper has been withdrawn by the authors. We withdraw our paper due to the acceptance in the journal "Applied Mathematics Letters" with a different title. r has been withdrawn by the authors due to a