The concept of lacunary statistical convergence was introduced in intuitionistic fuzzy n-normed spaces in Sen and Debnath (Math. Comput. Model. 54:2978-2985. In this article, we introduce the notion of lacunary -statistically convergent and lacunary -statistically Cauchy sequences in an intuitionistic fuzzy n-normed space. Also, we give their properties using lacunary density and prove relation between these notions. MSC: 47H10; 54H25

We define generalized paranormed sequence spaces c σ, M, p, q, s , c 0 σ, M, p, q, s , m σ, M, p, q, s , and m 0 σ, M, p, q, s defined over a seminormed sequence space X, q . We establish some inclusion relations between these spaces under some conditions.

In this paper, we introduce the concepts of $\alpha\beta-$statistical convergence and strong $\alpha \beta-$Ces\`{a}ro summability of delta measurable functions on anarbitrary time scale. Then some inclusion relations and results about these new concepts are presented. We will also investigate the relationship between statistical convergence and $\alpha \beta-$statistical convergence on a time scale.

This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence and m -lacunary strongly summable with respect to a modulus f . Using this definitions we have proved the ( f, m )-asymptotically equivalence and m -lacunary statistical asymptotically equivalence analogues of theorems of Tripathy and Et (Stud Univ Babeş-Bolyai Math (1): [119][120][121][122][123][124][125][126][127][128][129][130] 2005) and Çolak's theorems (Filomat 17:9-14, 2003).

The purpose of the paper is to introduce the concepts of almost λ -statistical convergence and strongly almost λ -convergence of sequences of fuzzy numbers. We establish some connections between these concepts. It is also shown that if a sequence of fuzzy numbers is strongly almost λ -convergent with respect to a sequence of Orlicz funtions then it is almost λ -statistical convergent.