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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 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 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]