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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 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]

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]