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.

arXiv comment19 pages. arXiv admin note: substantial text overlap with arXiv:1307.5817, arXiv:1307.6208, arXiv:1307.5883