Nörlund statistical convergence and Tauberian conditions for statistical convergence from statistical summability using Nörlund means in non-Archimedean fields

Volume 24, Issue 4, pp 299--307 http://dx.doi.org/10.22436/jmcs.024.04.02

Publication Date: April 05, 2021 Submission Date: January 07, 2021 Revision Date: February 19, 2021 Accteptance Date: February 21, 2021

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Authors

D. Eunice Jemima - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, India. V. Srinivasan - (Retd. Professor) Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, India.

Abstract

In this paper, we define the concept of statistical convergence of sequences by Nörlund summability method and obtain a few results on the relationship between Nörlund summability and Nörlund statistical convergence in a complete, non-trivially valued, non-Archimedean field \(K\). Also, the necessary and sufficient Tauberian conditions under which statistical convergence follows from statistical summability by Nörlund means over \(K\) are discussed.

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Keywords

• Non-Archimedean fields
• Nörlund mean
• statistical convergence
• statistical summability \((N, p_n)\)
• Tauberian conditions

MSC

•  40A35
•  40E05
•  40G05
•  40G15
•  46S10

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