Double sequence spaces and Riesz mean

The present thesis consists of six chapters and is organized as follows: In Chapter 1, we summarize the main results of this study. In the second Chapter, we give definitions and theorems about our subject are available in present literature. In Chapter 3, as the domain of four dimensional Riesz mean $R^{qt}$ in the spaces $\mathcal{M}_u$, $\mathcal{C}_p$, $\mathcal{C}_{bp}$ and $\mathcal{C}_{r}$, we define the double sequence spaces $R^{qt}(\mathcal{M}_u)$, $R^{qt}(\mathcal{C}_p)$, $R^{qt}(\mathcal{C}_{bp})$ and $R^{qt}(\mathcal{C}_{r})$, and also examine some properties of those sequence spaces. In Chapter 4, we introduce the double sequence space $R^{qt}(\mathcal{L}_{s})$ as the domain of four dimensional Riesz mean $R^{qt}$ in the space $\mathcal{L}_{s}$ of absolutely $s$-summable double sequences and give some topological properties. In Chapter 5, we determine the $\alpha$-dual, $\gamma$-dual and $\beta(\vartheta)-$dual of the spaces $R^{qt}(\mathcal{M}_u)$, $R^{qt}(\mathcal{C}_{p})$, $R^{qt}(\mathcal{C}_{bp})$, $R^{qt}(\mathcal{C}_{r})$ and $R^{qt}(\mathcal{L}_s)$ for $0