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}k∈N 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)) of (dual) multi-generalized 2-normed space 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 defined on a proper commutative H∗ -algebra.