Mathematics and Statistics Vol. 10(5), pp. 988 - 994
DOI: 10.13189/ms.2022.100510
Reprint (PDF) (241Kb)

On -Ideal Statistically Convergent of Double Sequences in n-Normed Spaces over Non-Archimedean Fields

R. Sakthipriya , K. Suja ^*
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, India

ABSTRACT

The main aim of this work is to investigate some important properties of statistical convergence sequence in non-Archimedean fields. Statistical convergence has been discussed in various fields of mathematics namely approximation theory, measure theory, probability theory, trigonometric series, number theory, etc. The concept of summability over valued fields is a significant area of mathematics that has many applications in analytic continuation, quantum mechanics, probability theory, Fourier analysis, approximation theory, and fixed point theory. The theory of statistical convergence plays a notable space in the summability theory and functional analysis. The purpose of this work is to provide certain characterizations of ideal statistical convergence of sequence and ideal statistical Cauchy sequence in n-normed spaces and the establishment of relevant results in non-Archimedean fields. The ideal statistical convergence of sequence and ideal statistically Cauchy sequence are defined. A few related theorems are proved in field . The results of this work are extended to establish statistical convergence of double sequences in n-normed space and some new results have been proved. In this work, the main concept is ideal statistical convergence of double sequences in n-normed space over a complete, non-trivially valued, non-Archimedean field. Throughout this article, is a complete, non-trivially valued, non-Archimedean field.

KEYWORDS
Statistical convergence, Ideal, Ideal convergent, Double Sequences, n-Normed Space, Non-Archimedean Fields

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R. Sakthipriya , K. Suja , "On -Ideal Statistically Convergent of Double Sequences in n-Normed Spaces over Non-Archimedean Fields," Mathematics and Statistics, Vol. 10, No. 5, pp. 988 - 994, 2022. DOI: 10.13189/ms.2022.100510.

(b). APA Format:
R. Sakthipriya , K. Suja (2022). On -Ideal Statistically Convergent of Double Sequences in n-Normed Spaces over Non-Archimedean Fields. Mathematics and Statistics, 10(5), 988 - 994. DOI: 10.13189/ms.2022.100510.