Difference Sequence Spaces Derived by Using Generalized Means

This paper deals with new sequence spaces $X(r, s, t ;Δ)$ 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 $X(r, s, t ;Δ)$ for $X\in \{c, c_0\}$ have Schauder basis. Furthermore, the $α$-, $β$-, $γ$- duals of these sequence spaces are computed and also established necessary and sufficient conditions for matrix transformations from $X(r, s, t ;Δ)$ to $X$.

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