Difference Sequence Spaces Derived by Using Generalized Means

Abstract: This paper deals with new sequence spaces $X(r, s, t ;\Delta) $ for $X\in {l_\infty, c, c_0}$ defined by using generalized means and difference operator. It is shown that these spaces are complete normed linear spaces and the spaces $X(r, s, t ;\Delta)$ for $X\in {c, c_0}$ have Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also established necessary and sufficient conditions for matrix transformations from $X(r, s, t ;\Delta)$ to $X$.