On the Domain of the Fibonacci Difference Matrix

Fevzi Yaşar and Kuddusi Kayaduman
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Fevzi Yaşar: Kilis Yatırım Destek Ofisi, Şehitler Mah. Cambazlar Sok. No:9, Kilis 79000, Turkey
Kuddusi Kayaduman: Faculty of Arts and Sciences, Department of Mathematics, Gaziantep University, Gaziantep 27310, Turkey

Mathematics, 2019, vol. 7, issue 2, 1-16

Abstract: 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, Ba?ar?r 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, Ya?ar 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.

Keywords: matrix transformations; Fibonacci numbers; sequence spaces; Fibonacci double band matrix; ?, ?, ? -duals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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