Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers

We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results

I_2-Convergence and I_2-Cauchy double sequences

In this article, we prove a decomposition theorem for I2-convergent double sequences and introduce the notions of I2-Cauchy and I 2 -Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I2, I)- convergence and (I2, I)-Cauchy double sequence

On Kuratowski i-convergence of sequences of closed sets

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Bas¸ar) to I− inner and I− outer limits and give some I− analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where I is an ideal of subsets of the set N of pos- itive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski I− convergence for a sequence of closed sets and get some properties for Kuratowski I− convergent sequences. Also, we examine the relationship between Kuratowski I− convergence and Hausdorff I− convergence

Lacunary Statistical Limit and Cluster Points of Generalized Difference Sequences of Fuzzy Numbers

The aim of present work is to introduce and study lacunary statistical limit and lacunary statistical cluster points for generalized difference sequences of fuzzy numbers. Some inclusion relations among the sets of ordinary limit points, statistical limit points, statistical cluster points, lacunary statistical limit points, and lacunary statistical cluster points for these type of sequences are obtained