λ (Δim)-Statistical Convergence of Order α.

In this study, using the generalized difference operator Δ^m_i and a sequence λ = (λ_n) which is a non-decreasing sequence of positive numbers tending to 8 such that λ_n+1 = λ_n + 1, λ₁ = 1, we introduce the concepts of λ(Δ^m_i) -statistical convergence of order α (α Є (0,1]) and strong λ (Δ^m_i) -Cesaro summablility of order α (α > 0). We establish some connections between λ (Δ_i^m) -statistical convergence of order a and strong λ (Δ^m_i) - Cesaro summablility of order a. It is shown that if a sequence is strongly λ (Δ^m_i) -Cesaro summable of order a, then it is λ (Δ_i^m) - statistically convergent of order i in case 0 < α ≤ β ≤ 1. [ABSTRACT FROM AUTHOR]