Some results on matrix transformation and compactness for fibonomial sequence spaces

In this paper, we introduce the Fibonomial sequence spaces \(b_{0}^{r,s,F}\) and \(b_{c}^{r,s,F}\) and show that these are linearly isomorphic to the spaces \(c_{0}\) and c,  respectively. In addition, we present \(\alpha -\)dual, \(\beta -\)dual and \(\gamma -\)dual for those spaces and characterize certain matrix classes. In the final section, we obtain some criteria for the compactness of certain matrix operators via Hausdorff measure of noncompactness on the space \(b_{0}^{r,s,F}.\)