On ideal convergence Fibonacci difference sequence spaces

Abstract

Abstract The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the Fibonacci difference matrix F̂ by using the Fibonacci sequence (fn) $(f_{n})$ for n∈{0,1,…} $n\in{\{0, 1, \ldots\}}$ and introduced new sequence spaces related to the matrix domain of F̂. In this paper, by using the Fibonacci difference matrix F̂ defined by the Fibonacci sequence and the notion of ideal convergence, we introduce the Fibonacci difference sequence spaces c0I(Fˆ) $c^{I}_{0}(\hat {F})$, cI(Fˆ) $c^{I}(\hat{F})$, and ℓ∞I(Fˆ) $\ell^{I}_{\infty}(\hat{F})$. Further, we study some inclusion relations concerning these spaces. In addition, we discuss some properties on these spaces such as monotonicity and solidity.

Keywords

• Fibonacci difference matrix
• Fibonacci I-convergence
• Fibonacci I-Cauchy
• Fibonacci I-bounded
• Lipschitz function