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On the Domain of the Fibonacci Difference Matrix

Author

Listed:
  • 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)

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, 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.

Suggested Citation

  • Fevzi Yaşar & Kuddusi Kayaduman, 2019. "On the Domain of the Fibonacci Difference Matrix," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:204-:d:208107
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    References listed on IDEAS

    as
    1. Mehmet Şengönül & Kuddusi Kayaduman, 2012. "On the Riesz Almost Convergent Sequences Space," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, May.
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