Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
I-localized Sequence in Two Normed Spaces
Yamanci, U., Savas, E., and Gürdal, M.
Corresponding Email: ulasyamanci@sdu.edu.tr
Received date: 3 July 2019
Accepted date: 27 August 2020
Abstract:
In this paper, our aim is to introduce the \(\mathcal{I}\)-localized and the \(\mathcal{I}\)-localized sequences in 2-normed spaces and study the fundamental properties of \(\mathcal{I}\)-localized sequences. Under some conditions, we show that \(\mathcal{I}\)-localized sequence is an \(\mathcal{I}\)-Cauchy sequence. Furthermore, the definition of uniformly \(\mathcal{I}\)-localized sequences in 2-normed spaces is given, and some results related with this concept are obtained.
Keywords: Ideal convergence, 2-normed space, ideal localor of the sequence, Cauchy sequence, uniformly localized sequence
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