Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
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

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences