IJPAM: Volume 25, No. 1 (2005)

ON SOME DIFFERENCE SEQUENCE SPACES
GENERATED BY INFINITE MATRICES

Murat Candan$^1$, Ihsan Solak$^2$
$^{1,2}$Department of Mathematics
Inönü Universty
Malatya, 44069, TURKEY
$^1$e-mail: mcandan@inonu.edu.tr
$^2$e-mail: isolak@inonu.edu.tr


Abstract.The sequence spaces $\left( \hat{A},p,\Delta\right) _{0},~\left( \hat
{A},p,\Delta\right)$ and $\left( \hat{A},p,\Delta\right) _{\infty}$ were studied Solak [16]. The main purpose of the present paper is to introduce the spaces $\left( \hat{A},p,\Delta^{r}\right) _{0},~\left( \hat{A}%
,p,\Delta^{r}\right)$ and $\left( \hat{A},p,\Delta^{r}\right) _{\infty}$ consisting of all sequences whose differences are in the spaces $\left( \hat{A},p,\Delta\right) _{0},~\left( \hat
{A},p,\Delta\right)$ and $\left( \hat{A},p,\Delta\right) _{\infty}$, respectively, and to fill up the gap in the existing literature. Also, we investigate some properties of these spaces. Our results are more general than some theorems of Nanda [13] and Solak [16].

Received: September 10, 2005

AMS Subject Classification: 46A45

Key Words and Phrases: sequence spaces, linear topological space, paranorm

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 1