## Taiwanese Journal of Mathematics

### SPACES OF CESÀRO DIFFERENCE SEQUENCES OF ORDER $r$ DEFINED BY A MODULUS FUNCTION IN A LOCALLY CONVEX SPACE

Mikail Et

#### Abstract

The idea of difference sequence spaces was introduced by Kizmaz [12] and was generalized by Et and Colak [6]. In this paper we introduce and examine some properties of the sequence spaces $\left[ V,\lambda,f,p \right]_{0} \left( \Delta_{v}^{r},q \right)$, $\left[ V,\lambda,f,p \right]_{1} \left( \Delta_{v}^{r},q \right)$, $\left[ V,\lambda,f,p \right]_{\infty} \left( \Delta_{v}^{r},q \right)$, $S_{\lambda}(\Delta_{v}^{r},q)$ and give some inclusion relations on these spaces. We also show that the space $S_{\lambda}(\Delta_{v}^{r},q)$ may be represented as a $\left[ V,\lambda,f,p \right]_{1} \left( \Delta_{v}^{r},q \right)$ space. Furthermore, we compute Köthe-Toeplitz duals of the spaces of generalized Cesàro difference sequences spaces.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 4 (2006), 865-879.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403878

Digital Object Identifier
doi:10.11650/twjm/1500403878

Mathematical Reviews number (MathSciNet)
MR2229627

Zentralblatt MATH identifier
1149.46008

#### Citation

Et, Mikail. SPACES OF CESÀRO DIFFERENCE SEQUENCES OF ORDER $r$ DEFINED BY A MODULUS FUNCTION IN A LOCALLY CONVEX SPACE. Taiwanese J. Math. 10 (2006), no. 4, 865--879. doi:10.11650/twjm/1500403878. https://projecteuclid.org/euclid.twjm/1500403878

#### References

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