(∆_v^m )_u-Statistical Boundedness and Convergence of Order 𝛂

In this paper, we defined the concepts of (∆_v^m )_u-statistical convergence and (∆_v^m )_u-statistical boundedness for sequences u and v with nonzero terms. Then, we extend these concepts to the concepts of (∆_(λ,v)^m )_u-statistical convergence and (∆_(λ,v)^m )_u-statistical boundedness using the sequences (λ_n) satisfying the conditions λ_1=1, λ_(n+1)≤λ_n+1 and λ_n→∞ (n→∞). Then, using the concepts of (∆_(λ,v)^m )_u-statistical convergence and (∆_(λ,v)^m )_u-statistical boundedness, we defined the sequence spaces (∆_(λ,v)^m )_u (S_c^α) and (∆_(λ,v)^m )_u (S_b^α) with the help of numbers α satisfying the condition 0