Main Article Content
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 ∥.∥∞.
Maddox IJ. Some properties of paranormed sequence spaces. J. London. Math.Soc. 1969;1:316- 322.
Fridy JA. Orhan C. Lacunary statistical convergence. Pacific J. Math. 1993;160:43-51.
Kostyrko P, Sal´at T, Wilczy´nski W. I-convergence. Real Anal. Exch. 2000;26(2):669-686. ˇ
Demirci K. I-limit superior and limit inferior. Math. Commun. 2001;6:165-172.
Das P, Kostyrko P, Malik P, Wilczy´nski W. I and I∗-convergence of double sequences. Math. Slovaca. 2008;58:605-620.
Sˇal´ at T, Tripathy BC, Ziman M. On some properties of I-convergence. Tatra Mt. Math. Publ. 2004;28:279-286.
Khan N. Classes of i-convergent double sequences over n-normed spaces. Journal of Function Spaces. 2016;7. Article ID 7594031 Available:https://doi.org/10.1155/2016/7594031
S¸ahiner A, G¨urdal M. Ideal convergence in n-normed spaces and some new sequence spaces via n-norm. Journal of Fundamental Sciences. 2008;4:233-244.
G¨ahler S. Linear 2-normietre. R¨ame, Math. Nachr. 1965;28;1-43.
Misiak A. n-inner product spaces. Math. Nachr. 1989;140;299-319.
Gunawan H. The space of p-summable sequence and its natural n-norm. Bull. Aust. Math. Soc. 2001;64;137-147.
Gunawan H. n-inner product, n-norms and the Cauchy-Schwartz inequality. Sci. Math. Jpn. 2001;5:47-54.
Gunawan H, Mashadi. On n-normed spaces. Int. J. Math. Sci. 2001;27:631-639.
Yamanci U, Gurdal M. I-statistical convergence in 2-normed space. Arab Journal of Mathematical sciences. 2014;20(1):41-47.
Sava¸s E. Some new sequence spaces defined by bounded variation in 2-normed spaces. Filomat. 2019;33(2):483-492.
Sava¸s E. On two-valued measure and double statistical convergence in 2-normed spaces. J. Inequal. Appl. 2013;347:11.
Sava¸s E. Some new double sequence spaces defined by orlicz function in n-normed space. Journal of inequalities and applications; 2011. Article Number: 592840