Δ^{m}-statistical boundedness of order α

In this dissertation, initially we define Δ^{m}-statistical boundedness by using the generalized difference operator Δ^{m} and examine its relationship between Δ^{m}-statistical convergence, Δ^{m}-Cauchiness and Δ^{m}-statistical boundedness. Plus, we give a useful characterization for a sequence x=(x_{k}) to be Δ^{m}-statistically bounded. Afterwards we compute the Köthe-Toeplitz and the generalized Köthe-Toeplitz duals of the set of all Δ^{m}-statistical bounded sequences. Being motivated by this we come up with the idea of statistical Köthe-Toeplitz and statistical generalized Köthe-Toeplitz duals and deal some relevant concepts and properties. The statistical Köthe-Toeplitz and the statistical generalized Köthe-Toeplitz duals of c₀, c, ℓ_{∞}, Sc₀, Sc and S_{b} are also computed. Finally Δ^{m}-statistical boundedness is generalized with respect to α-density and λ-statistical sense and some inclusion theorems are discussed.