Statistical convergence of order $$\left( \beta ,\gamma \right) $$ β , γ 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 $$\left( \beta ,\gamma \right) $$ and strongly p-Cesaro summability of order $$\left( \beta ,\gamma \right) $$ are introduced for sequences of fuzzy numbers, where $$\alpha $$ and $$\beta $$ real numbers such that $$0<\alpha \le \beta \le 1$$ and some relations between statistical convergence of order $$\left( \beta ,\gamma \right) $$ and strongly p-Cesaro summability of order $$\left( \beta ,\gamma \right) $$ are given. Furthermore, it is shown that a bounded and statistically convergent sequence of fuzzy numbers need not strongly p-Cesaro summable of order $$\left( \beta ,\gamma \right) $$ in general for $$0<\beta \le \gamma \le 1$$ .