Multi-Generalized 2-Normed Space

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...

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Bibliographic Details
Published in:Filomat 2017-01, Vol.31 (3), p.841-851
Main Authors: Khanehgir, Mahnaz, Khibary, Marzieh Moradian, Hasanvand, Firoozeh, Modabber, Ahmad
Format: Article
Language:English
Subjects:
Mathematical sequences
Online Access:Get full text
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Summary: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.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1703841K