ON THE SPACES OF FIBONACCI DIFFERENCE ABSOLUTELY p-SUMMABLE, NULL AND CONVERGENT SEQUENCES

Let 0 < p < 1. In the present paper, as the domain of the band matrix F̂ defined by the Fibonacci sequence in the classical sequence spaces `p, c0 and c, we introduce the sequence spaces `p(F̂ ), c0(F̂ ) and c(F̂ ), respectively. Also, we give some inclusion relations and construct the bases of the spaces c0(F̂ ) and c(F̂ ). Finally, we compute the alpha, beta, gamma duals of these spaces and characterize the classes (`p(F̂ ), μ) of infinite matrices with μ ∈ {`∞, c, c0}.