Statistical convergence of order (.,) for sequences of fuzzy numbers

Abstract

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 (ss,.) and strongly p-Cesaro summability of order (ss,.) are introduced for sequences of fuzzy numbers, where a and ss real numbers such that 0 < a = ss = 1 and some relations between statistical convergence of order (ss,.) and strongly p-Cesaro summability of order (ss,.) are given. Furthermore, it is shown that a bounded and statistically convergent sequence of fuzzy numbers need not strongly p-Cesaro summable of order (ss,.) in general for 0 < ss =. = 1.