Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$

Keywords: Statistical convergence, $(EC)_{n}^{1}-$ summability, $(EC)_{n}^{1}-$ statistically convergent, One-sided and two-sided Tauberian conditions

Abstract

Let $(x_k)$, for $k\in \mathbb{N}\cup \{0\}$  be a sequence of real or complex numbers and set $(EC)_{n}^{1}=\frac{1}{2^n}\sum_{j=0}^{n}{\binom{n}{j}\frac{1}{j+1}\sum_{v=0}^{j}{x_v}},$ $n\in \mathbb{N}\cup \{0\}.$  We present necessary and sufficient conditions, under which $st-\lim_{}{x_k}= L$ follows from $st-\lim_{}{(EC)_{n}^{1}} = L,$ where L is a finite number. If $(x_k)$ is a sequence of real numbers, then these are one-sided Tauberian conditions. If $(x_k)$ is a sequence of complex numbers, then these are two-sided Tauberian conditions.

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Author Biographies

Naim L. Braha, College Vizioni per Arsim Department of Computer Sciences and Applied Mathematics
Republic of Kosovo
Ismet Temaj, University of Prizren Faculty of Education
Republic of Kosovo
Published
2018-01-09
Section
Articles