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 1209.40003
Mursaleen, M.; Mohiuddine, S.A.
Invariant mean and some core theorems for double sequences.
(English)
[J] Taiwanese J. Math. 14, No. 1, 21-33 (2010). ISSN 1027-5487

A bounded double sequence $x=(x_{jk})$ of real numbers is said to be $\sigma-$convergent to a number $L$ if $x\in V_2^\sigma$ with $$V_{2}^{\sigma}= \bigg\{x: \lim_{p,q\to \infty}\frac{1}{(p+1)(q+1)}\sum_{j=0}^p\sum_{k=0}^q x_{\sigma^j(s),\sigma^k(t)}=L\text{ uniformly in }s,t;\ L=\sigma-\lim x\bigg\},$$ where $\sigma^p(k)$ denotes the $p$th iterate of the mapping $\sigma$ at $k$, and $\sigma^p(k)\neq k$ for all integer $k\geq 0$, $p\geq1$. In this paper the authors define and characterize the class $(V_2^{\sigma},V_2^{\sigma})$ and establish a core theorem. They determine a Tauberian condition for core inclusion and core equivalence.
[Umit Totur (Aydin)]
MSC 2000:
*40C05 Matrix methods in summability
40H05 Functional analytic methods in summability
40B05 Multiple sequences and series
40E05 Tauberian theorems, general

Keywords: double sequence; $p$-convergence; invariant mean; $\sigma$-convergence; $\sigma$-core; core theorems

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