Mathematics and Statistics Vol. 11(3), pp. 586 - 591
DOI: 10.13189/ms.2023.110316
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Statistical Convergence on Intuitionistic Fuzzy Normed Spaces over Non-Archimedean Fields

N. Saranya , K. Suja ^*
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203, India

ABSTRACT

This paper aims to explore the fundamental properties of statistical convergence sequences within non-Archimedean fields. In pure mathematics, statistical convergence plays a fundamental role. The idea of statistical convergence is an extension of the concept of convergence. Statistical convergence has been discussed in various fields of mathematics namely ergodic theory , fuzzy set theory, approximation theory, measure theory, probability theory, trigonometric series, number theory, and banach spaces, where problems were resolved using the concept of statistical convergence. Summability theory and functional analysis are two disciplines that heavily rely on the idea of statistical convergence. The study of analysis over non-Archimedean fields is called non-Archimedean analysis. The theory of statistical convergence plays a significant role in the functional analysis and summability theory. The objective of this paper is to expand upon the concepts of statistical convergence and statistically Cauchy sequences in non-Archimedean intuitionistic fuzzy normed spaces, and obtain some relevant results related to them. This article proves that some properties of statistically convergent sequences, which are not true classically, are true in a non-Archimedean field. Furthermore, in these spaces, we defined statistically complete and statistically continuous and established some fundamental facts. Throughout this paper, denotes a complete, non-trivially valued, non-Archimedean field.

KEYWORDS
Non-Archimedean Fields, Statistically Convergent, Statistically Cauchy Sequence, Intuitionistic Fuzzy Normed Spaces

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] N. Saranya , K. Suja , "Statistical Convergence on Intuitionistic Fuzzy Normed Spaces over Non-Archimedean Fields," Mathematics and Statistics, Vol. 11, No. 3, pp. 586 - 591, 2023. DOI: 10.13189/ms.2023.110316.

(b). APA Format:
N. Saranya , K. Suja (2023). Statistical Convergence on Intuitionistic Fuzzy Normed Spaces over Non-Archimedean Fields. Mathematics and Statistics, 11(3), 586 - 591. DOI: 10.13189/ms.2023.110316.