# Statistical convergence of order \(\left( \beta ,\gamma \right) \) for sequences of fuzzy numbers

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## 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*-Cesàro 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*-Cesàro 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*-Cesàro summable of order \(\left( \beta ,\gamma \right) \) in general for \(0<\beta \le \gamma \le 1\).

## Keywords

Fuzzy number Fuzzy sequence Statistical convergence Cesàro summability## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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