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In this study we introduce the concepts of Wijsman asymptotically deferred statistical equivalence of order α and Wijsman strong deferred Cesàro asymptotically equivalence of order α for set sequences. [ABSTRACT FROM AUTHOR]

The purpose of this work is to introduce the concepts of …-lacunary statistical convergence of order α and lacunary strongly (…)-convergence of order α. We establish some connections between lacunary strongly (…) - convergence of order α and (…)-lacunary statistical convergence of order α. It is shown that if a sequence is lacunary strongly (…)-summable of order α then it is (…)-lacunary statistically convergent of order α. [ABSTRACT FROM AUTHOR]

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

The main purpose of this paper is to introduce the concepts of f-lacunary statistical convergence of order (α, β) and strong f--lacunary summability of order (α, β) of sequences of real numbers for 0 < a ≤ β ≤ 1, where f is an unbounded modulus. [ABSTRACT FROM AUTHOR]

In this study using the generalized difference operator Δm, we generalize the concepts of statistical convergence sequences of order α and statistical Cauchy sequences of order α. It is shown that, Δpm-statistically convergent sequences of order α and Δpm-statistical Cauchy sequences of order α are equivalent. [ABSTRACT FROM AUTHOR]