Difference Sequence Spaces Derived by Using Generalized Means

Atanu Manna; Amit Maji; P. D. Srivastava

doi:10.1016/j.joems.2014.02.010

paper

Difference Sequence Spaces Derived by Using Generalized Means

arXiv:1307.6208 · doi:10.1016/j.joems.2014.02.010

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 $X$ .

arXiv comment15 pages. arXiv admin note: substantial text overlap with arXiv:1307.5817, arXiv:1307.5883, arXiv:1307.5884