Tauberian Conditions under which Statistical Convergence Follows from Statistical Summability by Weighted Means in Non-Archimedean Fields

Vaithinathasamy Srinivasan, D. Eunice Jemima

Abstract

In this paper, $K$ denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in $K$. The weighted statistical convergence and statistical summability were enunciated along with the notion of $(\N, p_n)$ - summability method in [K. Suja, V. Srinivasan, Weighted statistical convergence in ultrametric fields, International Journal of Pure and Applied Mathematics 116 (4) (2017) 813--817]. We have proved here, the necessary and sufficient Tauberian conditions under which statistical convergence follows from statistical summability by weighted means over non-archimedean fields (an analogous and further extension of these concepts proved by F. Moricz and C. Orhan [F. Moricz, C. Orhan, Tauberian conditions under which statistical convergence follows from statistical summability by weighted means, Studia Sci. Math. Hung. 41 (4) (2004) 391--403], in the classical context).