Affiliation:
1. Islamic Azad University, Mashhad Branch, Department of Mathematics, Mashhad, Iran
2. Farhangian University, Department of Pure Mathematics, Mashhad, Iran
Abstract
In this paper, we introduce the concepts of multi-generalized 2-normed space
and dual multigeneralized 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.
Publisher
National Library of Serbia