On statistical convergence of double sequences of closed sets

In this paper, we introduce the concepts of statistical inner and statistical outer limits for double sequences of closed sets and give some formulas for finding these limits. Also, we give the Kuratowski statistical convergence of double sequences of sets by means of the statistical inner and statistical outer limits of a double sequence of closed sets

I_2-Cauchy double sequences of fuzzy numbers

In this paper, we introduce the concepts of I2-Cauchy, I∗2-Cauchy double sequence of fuzzy numbers and study their some properties and relations, where I2 denotes the ideal of subsets of N × N

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

E-core of double sequences

Boos, Leiger and Zeller [1,2] defined the concept of e-convergence. In this paper we introduce the concepts of e-limit superior and inferior for real double sequences and prove some fundamental properties of e-limit superior and inferior. In addition to these results we define e-core for double sequences. Also, we show that that if A is a nonnegative C e -regular matrix then the e-core of Ax is contained in e-core of x, provided that Ax exists

On statistically convergent sequences of closed sets

In this paper, we give the definitions of statistical inner and outer limits for sequences of closed sets in metric spaces. We investigate some properties of statistical inner and outer limits. For sequences of closed sets if its statistical outer and statistical inner limits coincide, we say that the sequence is Kuratowski statistically convergent. We prove some proporties for Kuratowski statistically convergent sequences. Also, we examine the relationship between Kuratowski statistical convergence and Hausdorff statistical convergence

Necessary and sufficient Tauberian conditions for the A^r method of summability

Móricz and Rhoades determined the necessary and sufficient Tauberian conditions for certain weighted mean methods of summability in [Acta. Math. Hungar. 102(4) (2004), 279{285]. In the present paper, we deal with the necessary and sufficient Tauberian conditions for the Ar method which was introduced by Bas̨ar in [Fırat Üniv. Fen & Müh. Bil. Dergisi 5(1)(1993), 113{117]

On the Slowly Decreasing Sequences of Fuzzy Numbers

We introduce the slowly decreasing condition for sequences of fuzzy numbers. We prove that this is a Tauberian condition for the statistical convergence and the Cesáro convergence of a sequence of fuzzy numbers

I_2-Convergence of double sequence of fuzzy numbers

In this paper, we introduce and study the concepts of I_2-convergence, I∗_2-convergence for double sequences of fuzzy real numbers, where I_2 denotesthe ideal of subsets of N × N. Also, we study some properties and relations of them