Non-equivalent n-norms being Sequentially Equivalent

Abstract

In [4], we have already studied the space of p-summable sequences i.e. (lp)
as an n-normed space by dening a new n-norm on it. In [5], we have resulted
that equivalent norms can be derived by non-equivalent n-norms. Inspired by the
problem raised in Gunawan and others paper [7], in this paper, we shall show
that sequentially equivalent n-norms need not be equivalent.