Difference Sequence Spaces Derived by Using Generalized Means

Abstract

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 $X$.

15 pages. arXiv admin note: substantial text overlap with arXiv:1307.5817, arXiv:1307.5883, arXiv:1307.5884