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.Downloads
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Published
2018-01-09
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