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The main object of this article is to introduce the concepts of (f, ρ)- statistical convergence of order α and strong (f, ρ)- summability of order α of sequences of real numbers and give some inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In this study, by using definition of ρ-statistical convergence which defined by Çakallı [5] we introduce the concepts of pointwise w ρ α (f) -summability, pointwise ρ-statistical convergence of order α and uniform ρ-statistical convergence of order α sequences of real-valued functions. Also, we give some inclusion relations between these concepts. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce the concepts of Wijsman deferred statistical convergence of order α and Wijsman strong deferred Cesàro convergence of order α for sequences of sets. [ABSTRACT FROM AUTHOR]

In this study, we introduce and examine the concepts of Δm−weighted statistical convergence and Δm−weighted (N ¯ , p n) −summability. Also some relations between Δm−weighted statistical convergence and Δm−weighted (N ¯ , p n) −summability are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of Δα-deferred statistical convergence with the fractional order of α and Δα- strongly convergence with the fractional order of α. Additionally, we give some relations about these concepts. [ABSTRACT FROM AUTHOR]

In this study, by using definition of ρ-statistical convergence which was defined by Ç akallı[2], we give some inclusion relations between the set of ρ-statistical convergence and strong (S, [ρ]) summability. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of strong ρ−convergence of order β (or N p β (ρ) −convergence) of sequence of real numbers and give some inclusion relations between the set of all ρ−statistical convergence of order β and strong N p β (ρ)− convergence. [ABSTRACT FROM AUTHOR]

Abstract. In this study, using a lacunary sequence we introduce the concepts of lacunary d−statistically convergent sequences and lacunary d−statistically bounded sequences in general metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, the concept of deferred statistical convergence of order α is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order α in topological groups and the set of all deferred statistically convergent sequences of order α in topological groups are given. [ABSTRACT FROM AUTHOR]

In this paper, the definitions of lacunary strong A−convergence of order (α, β) with respect to a modulus and lacunary A−statistical convergence of order (α, β) are given. We study some connections between lacunary strong A−convergence of order (α, β) with respect to a modulus and lacunary A−statistical convergence of order (α, β). [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and investigate the concepts of deferred strong summability and deferred statistical convergence of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between deferred strong summability and deferred statistical convergence of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞) are also given. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The idea of I−convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P., Šalát, T. and Wilczyński, W. I−convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle, W. H. Generalized statistical convergence and convergence free spaces. J. Math. Anal. Appl. 245(2) (2000), 513–527]. In this paper we introduce I−deferred statistical convergence and strong I−deferred Cesàro convergence and investigate between their relationship. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concepts of Wijsman (f, I) −lacunary statistical convergence of order α and Wijsman strongly (f, I) −lacunary statistical convergence of order α, and investigated between their relationship. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (α, β) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (α, β) is also investigated. Interesting results are obtained. [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]

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]