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

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.