### Journals Information

**
Mathematics and Statistics Vol. 11(1), pp. 128 - 133 DOI: 10.13189/ms.2023.110114 Reprint (PDF) (271Kb) **

## Some Results of Generalized Weighted Norlund-Euler- Statistical Convergence in Non-Archimedean Fields

**Muthu Meena Lakshmanan E , Suja K ^{*}**

Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, India

**ABSTRACT**

Non-Archimedean analysis is the study of fields that satisfy the stronger triangular inequality, also known as ultrametric property. The theory of summability has many uses throughout analysis and applied mathematics. The origin of summability methods developed with the study of convergent and divergent series by Euler, Gauss, Cauchy and Abel. There is a good number of special methods of summability such as Abel, Borel, Euler, Taylor, Norlund, Hausdroff in classical Analysis. Norlund, Euler, Taylor and weighted mean methods in Non-Archimedan Analysis have been investigated in detail by Natarajan and Srinivasan. Schoenberg developed some basic properties of statistical convergence and also studied the concept as a summability method. The relationship between the summability theory and statistical convergence has been introduced by Schoenberg. The concept of weighted statistical convergence and its relations of statistical summability were developed by Karakaya and Chishti. Srinivasan introduced some summability methods namely y-method, Norlund method and Weighted mean method in p-adic Fields. The main objective of this work is to explore some important results on statistical convergence and its related concepts in Non-Archimedean fields using summability methods. In this article, Norlund-Euler- statistical convergence, generalized weighted summability using Norlund-Euler- method in an Ultrametric field are defined. The relation between Norlund-Euler- statistical convergence and Statistical Norlund-Euler- summability has been extended to non-Archidemean fields. The notion of Norlund-Euler- statistical convergence and inclusion results of Norlund-Euler statistical convergent sequence has been characterized. Further the relation between Norlund-Euler- statistical convergence of order α & β has been established.

**KEYWORDS**

Weighted Norlund-Euler Statistical Convergence, NE-statistical Summable, Generalized Weighted Norlund-Euler--statistical Convergence, Non-Archimedean Field, Ultrametric Field

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Muthu Meena Lakshmanan E , Suja K , "Some Results of Generalized Weighted Norlund-Euler- Statistical Convergence in Non-Archimedean Fields," Mathematics and Statistics, Vol. 11, No. 1, pp. 128 - 133, 2023. DOI: 10.13189/ms.2023.110114.

(b). APA Format:

Muthu Meena Lakshmanan E , Suja K (2023). Some Results of Generalized Weighted Norlund-Euler- Statistical Convergence in Non-Archimedean Fields. Mathematics and Statistics, 11(1), 128 - 133. DOI: 10.13189/ms.2023.110114.