Multi-Generalized 2-Normed Space

Abstract

In this paper, we introduce the concepts of multi-generalized 2-normed space
and dual multi-generalized 2-normed space and we then investigate some results related to
them. We also prove that, if (E; ∥:; :∥) is a generalized 2-normed space, {∥:; :∥k}k2N is a
sequence of generalized 2-norms on Ek (k ∈ N) such that for each x; y ∈ E, ∥x; y∥1 =
∥x; y∥ and for each k ∈ N axioms (MG1); (MG2) and (MG4)( (DG4)) are true, then
{(Ek; ∥:; :∥k); k ∈ N} is a (dual) multi-generalized 2-normed space. Finally we deal with an
application of a dual multi-generalized 2-normed space dened on a proper commutative
H-algebra.