Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

Abstract

Abstract:In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically .C; 1; 1/ summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically .C; 1; 1/ summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively.

Statistical weighted mean summability of double sequences of fuzzy numbers

“…Furthermore, by combining our results with results of [30], we deduce that under Hardy conditions, u mn st −→ µ (N, p, q, 1, 1) implies validity of u mn −→ µ. Our results include the corresponding results in [21,34] for the case p j = 1 for all j and q k = 1 for all k.…”

“…However, the converses of these implications is false, in general. For the implication that u mn st −→ µ ⇒ u mn → µ several Tauberian results were found (see [21,30]). Also Totur and C ¸anak [33] have given Tauberian conditions under which…”

“…After this Yapalı ve Talo [34] and Önder at al. [21] presented statistical (C, 1, 1) summability method for double sequences of fuzzy numbers.…”

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

“…It follows from Theorem 2.6 of [6] and Example 4.2 of [19] that the converse implication of Theorem 2.4 does not hold in general. We nd some conditions under which the converse also holds.…”

“…In [24], Subrahmanyam dened the Cesàro summability method for sequences of fuzzy numbers and proved fuzzy analogues of some classical Tauberian theorems. For a detailed study and some results related to convergence of sequences of fuzzy numbers and Tauberian conditions, we refer to the papers [1,3,5,9,10,14,19,26].…”