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On a new type of generalized difference Cesàro sequence spaces. (English) Zbl 1093.46507
Summary: We introduce the generalized difference Cesàro sequence spaces $C_\infty (\Delta_m^n)$, $O_\infty(\Delta^n_m)$, $C_p(\Delta^n_m)$, $O_p(\Delta_m^n)$ and $\ell_p(\Delta^n_m)$ for $1\le p\le\infty$. We study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces. These notions generalize many notions on difference Cesàro sequence spaces.

46B45Banach sequence spaces
40A05Convergence and divergence of series and sequences
40C05Matrix methods in summability