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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]

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]

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]

In this study, we introduce the concepts of pointwise deferred statistical convergence and strongly deferred Cesàro pointwise summable sequences of fuzzy mappings. Some relations between pointwise deferred statistical convergence and strongly deferred Cesàro pointwise summable sequences of fuzzy mappings are given. [ABSTRACT FROM AUTHOR]

In this study, using a lacunary sequence we introduce the concepts of lacunary d−statistical convergence of order α and lacunary strong d p−Cesaro summability of order α in general metric spaces. [ABSTRACT FROM AUTHOR]

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]

In this study, we introduce and examine the concepts of △θm-asymptotically statistical equivalent of order a and strong △θm-asymptotically equivalent of order α of sequences. Also, we give some relations connected to these concepts. [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]

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]

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]

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 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]

We define the sequence spaces â„"âž (△p), c (△p) and c 0 (△p), give some topological properties and inclusion relations of these sequence spaces. [ABSTRACT FROM AUTHOR]