Abstract
In this article we introduce the generalized Fibonacci difference operator F(B) by the composition of a Fibonacci band matrix F and a triple band matrix B(x, y, z) and study the spaces l(k)(F(B)) and l(infinity)(F(B)). We exhibit certain topological properties, construct a Schauder basis and determine the Kothe-Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces l(k)(F(B)) and l(infinity)(F(B)) to space Y is an element of {l(infinity), c(0), c, l(1), cs(0), cs, bs} and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces l(k)(F(B)) and l(infinity)(F(B)) to Y is an element of {l(infinity), c, c(0), l(1), cs(0), cs, bs} using the Hausdorff measure of non-compactness.