On lacunary statistical convergence of order β of difference sequences of fractional order

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