On ideal convergence Fibonacci difference sequence spaces

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