Gülsen Kılınç, Murat Candan

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This paper submits the sequence space $l\left( \widehat{F}\left( r,s\right)
,\mathcal{F},p,u\right) $ and $l_{\infty }\left( \widehat{F}\left(
r,s\right) ,\mathcal{F},p,u\right) $of non-absolute type under the domain of
the matrix$\widehat{\text{ }F}\left( r,s\right) $ constituted by using
Fibonacci sequence and non-zero real number $r$, $s$ and a sequence of
modulus functions. We study some inclusion relations, topological and
geometric properties of these spaceses. Further, we give the $\alpha $- $%
\beta $- and $\gamma $-duals of said sequence spaces and characterization of
the classes $\left( l\left( \widehat{F}\left( r,s\right) ,\mathcal{F}%
,p,u\right) ,X\right) $ and $\left( l_{\infty }\left( \widehat{F}\left(
r,s\right) ,\mathcal{F},p,u\right) ,X\right) $.


Sequence space, Fibonacci sequence, Modulus functions


Fibonacci numbers, modulus function, sequence spaces, matrix transformations, $\alpha -,\beta -,\gamma -$ duals, difference matrix.

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