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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 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]

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, 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]