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$$\lambda$$-statistical convergence. (English) Zbl 0953.40002
This paper deals with a generalization of the Cesàro mean summability of the sequences $[C,1]:=\{x=(x_n): \text{ there is } L \in \mathbb{R}\text{ such that } \lim _{n \to \infty }{1 \over n} \sum _{k=1}^n {}x_k - L{}=0 \}$ to $[V,\lambda ]:= \{x=(x_n): \text{ there is } L \in \mathbb{R} \text{ such that } \lim_{n \to \infty }{1 \over \lambda _n} \sum _{k \in I_n} {}x_k - L{}=0{}\}$ for some interval $$I_n$$. Comparisons of statistical convergence and $$\lambda$$-statistical convergence for a sequence $$x=(x_n)$$ defined by using limits $\lim _{n \to \infty }{1 \over n} {}\{ k \leq n : {}x_n - L{} \geq \varepsilon \}=0 \quad \text{and}\quad\lim _{n \to \infty }{1 \over \lambda _n} {}\{k \in I_n : {}x_n - L{} \geq \varepsilon \}= 0$ are given.

##### MSC:
 40A05 Convergence and divergence of series and sequences 40C05 Matrix methods for summability
##### Keywords:
statistical convergence; summability of sequences
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##### References:
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