Some New Paranormed Difference Sequence Spaces Derived by Fibonacci Numbers

TL;DR

This paper introduces new paranormed sequence spaces based on Fibonacci numbers, analyzes their duals and bases, and characterizes matrix transformations to classical Maddox's spaces, expanding the understanding of Fibonacci-related sequence spaces.

Contribution

It presents novel paranormed sequence spaces derived from Fibonacci numbers and explores their duals, bases, and matrix transformations to classical sequence spaces.

Findings

Computed the $eta$-dual and $eta$-dual spaces.

Established bases for the new sequence spaces.

Characterized matrix transformations to Maddox's classical spaces.

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 $\ell_{\infty}(q)$.