Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

Abstract

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

Keywords

• Fibonacci numbers
• Difference matrix
• $\alpha$-,$\beta$-,$\gamma$-duals
• Matrix Transformations
• fixed point property
• Banach-Saks type $p.$