A Note on Convergence in Normed Hypervector Spaces

The aim of this paper is to introduce the concept of convergence of a sequence on hypernormed spaces and establish a few basic prop- erties of convergent sequences and Cauchy sequences on hypernormed spaces. Also we have established a necessary and su±cient condition for a Cauchy sequence to be convergent sequence in this spaces. In fact, also it has been shown that limit of a convergent sequence in such type spaces is not necessarily unique.