Matrix

*F*^{^} derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces

*l*_{p}(

*F)* and

*l*_{∞}(

*F)*; (1 ≤

*p* < ∞) were examined. Then, Başarır et al. (2015) defined the spaces

*c*_{}
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Matrix

*F*^{^} derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces

*l*_{p}(

*F)* and

*l*_{∞}(

*F)*; (1 ≤

*p* < ∞) were examined. Then, Başarır et al. (2015) defined the spaces

*c*_{0}(

*F)* and

*c*(

*F)* and Candan (2015) examined the spaces

*c*(

*F(r,s))* and

*c*_{0}(

*F(r,s)).* Later, Yaşar and Kayaduman (2018) defined and studied the spaces

*cs(F(s,r))* and

*bs(F(s,r)).* In this study, we built the spaces

*cs*(

*F)* and

*bs*(

*F)*. They are the domain of the matrix

*F* on

*cs* and

*bs*, where

*F* is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that

*cs*(

*F*) and

*bs*(

*F*) are Banach spaces. It is determined that they have the

*γ, β, α* -duals. In addition, the Schauder base of the space

*cs*(

*F)* are calculated. Finally, a number of matrix transformations of these spaces are found.

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