Some New Paranormed Difference Sequence Spaces Derived by Fibonacci Numbers

Abstract

In this study, we define new paranormed sequence spaces by the sequences of Fibonacci numbers. Furthermore, we compute the $\alpha -,\beta -$ and $\gamma -$ duals and obtain bases for these sequence spaces. Besides this, we characterize the matrix transformations from the new paranormed sequence spaces to the Maddox's spaces $c_0(q),c(q),\ell (q)$ and ${\ell }_{\infty }(q)$.

arXiv admin note: text overlap with arXiv:1105.3747 by other authors