Ideally Statistical Convergence in n-normed Space
Nazneen Khan *
Department of Mathematics, College of Science and Arts, Taibah University, Madina, Saudi Arabia.
Amani Shatarah
Department of Mathematics, College of Science and Arts, Taibah University, Madina, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
The aim of the article is to extend the concept of Ideally statistical convergence from 2 normed spaces to n-normed space. We have also study and prove some important algebraic and topological properties of Ideally-statistical convergence of real sequences in n-normed space. In the last part of this article we obtain a criterion for I-statistically Cauchy sequence in n-normed space to be I-statistically Cauchy with respect to ∥.∥∞.
Keywords: Statistical convergence, Ideal convergence, Filter, statistically Cauchy sequence, real sequences, n-normed space.