Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means

Abstract

This paper presents new sequence spaces $X(r, s, t, p ;\Delta)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete under a suitable paranorm. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;\Delta)$ to $X$. Finally, it is proved that the sequence space $l(r, s, t, p ;\Delta)$ is rotund when $p_n>1$ for all $n$ and has the Kadec-Klee property.