On Lacunary Statistical Convergence of Order β of Difference Sequences of Fractional Order.

The purpose of this paper is to introduce the concepts of Δ^α-lacunary statistical convergence of order β (0 < β ≤ 1) with the fractional order of α and Δ^α-lacunary strongly convergence of order β with the fractional order of α. We establish some connections between Δ^α-lacunary strongly convergence of order β and Δ^α-lacunary statistical convergence of order β. [ABSTRACT FROM AUTHOR]