On <img src=image/13427444_01.gif>-Ideal Statistically Convergent of Double Sequences in n-Normed Spaces over Non-Archimedean Fields

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 <img src=image/13427444_01.gif> ideal statistical convergence of sequence and <img src=image/13427444_01.gif> ideal statistical Cauchy sequence in n-normed spaces and the establishment of relevant results in non-Archimedean fields. The <img src=image/13427444_01.gif> ideal statistical convergence of sequence and <img src=image/13427444_01.gif> ideal statistically Cauchy sequence are defined. A few related theorems are proved in field <img src=image/13427444_02.gif>. 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 <img src=image/13427444_01.gif> ideal statistical convergence of double sequences in n-normed space over a complete, non-trivially valued, non-Archimedean field. Throughout this article, <img src=image/13427444_02.gif> is a complete, non-trivially valued, non-Archimedean field.