Some further remarks on ideal summability in 2-normed spaces

✍ Scribed by Pratulananda Das; Sudip Kumar Pal; Sanjoy Kr Ghosal

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 236 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.08.007

✦ Synopsis

Very recently ideals were used to study the summability of sequences in 2-normed spaces by Gurdal and Acik (2008) [18], Gurdal and Pehlivan (2004) [19] and Sahiner et al. (2007) [11], who investigated some convergence and Cauchy conditions (namely I-convergence and I * -convergence and Cauchy conditions). In this work we make some further investigations along these lines which provide answers to two important questions regarding I-Cauchy and I * -Cauchy sequences which were left unanswered. We then introduce new concepts of I-divergence and I * -divergence in 2-normed spaces and study some of their properties.