New structure of Fibonacci numbers using concept of Δ --operator

Abstract

The theory of sequence spaces is the fundamental of summability and applications to various sequences like Fibonacci sequences were deeply studied. In [A. H. Ganie, In: Matrix Theory-Applications and Theorems, \(\textbf{2018}\) (2018), 75--86], the author has analyzed the Fibonacci sequences and studied its various properties. By utilizing this concept, the notion of this paper is to introduce new scenario of spaces using Fibonacci numbers. By using Kizmaz operator, we shall introduce the difference sequence spaces \(c^{J}_{0}(\widetilde{\mho_g})\), \(c^{J}(\widetilde{\mho_g})\) and \(\ell^{J}_{\infty}(\widetilde{\mho_g})\) by involving Fibonacci sequence and the idea of ideal convergence. We will prove certain basic inclusion relations and study these for some topological properties.