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Zbl 0953.40002
Mursaleen
$\lambda $-statistical convergence. (English)
[J] Math. Slovaca 50, No.1, 111-115 (2000). ISSN 0139-9918; ISSN 1337-2211/e

This paper deals with a generalization of the Cesàro mean summability of the sequences $$ [C,1]:=\{x=(x_n): \text{ there is } L \in \bbfR\text{ such that } \lim _{n \to \infty }{1 \over n} \sum _{k=1}^n {}x_k - L{}=0 \}$$ to $$[V,\lambda ]:= \{x=(x_n): \text{ there is } L \in \bbfR \text{ such that } \lim_{n \to \infty }{1 \over \lambda _n} \sum _{k \in I_n} {}x_k - L{}=0{}\}$$ 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.
[Ondrej Kováčik (Žilina)]

MSC 2000:: *40A05 Convergence of series and sequences
40C05 Matrix methods in summability

Keywords: statistical convergence; summability of sequences

Cited in: Zbl pre06010532 Zbl 1220.40004 Zbl 1219.40004 Zbl 1206.40003

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