Statistical convergence of order β,γ for sequences of fuzzy numbers.

The concepts of statistical convergence and strong p-Cesaro summability of sequences of real numbers were introduced in literature independently, and it was shown that if a sequence is strongly p-Cesaro summable, then it is statistically convergent and also a bounded statistically convergent sequence must be p-Cesaro summable. In the present paper, two new concepts named statistical convergence of order β , γ and strongly p-Cesàro summability of order β , γ are introduced for sequences of fuzzy numbers, where α and β real numbers such that 0 < α ≤ β ≤ 1 and some relations between statistical convergence of order β , γ and strongly p-Cesàro summability of order β , γ are given. Furthermore, it is shown that a bounded and statistically convergent sequence of fuzzy numbers need not strongly p-Cesàro summable of order β , γ in general for 0 < β ≤ γ ≤ 1 . [ABSTRACT FROM AUTHOR]