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

Foundations

## 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

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

• Hifsi Altinok
• 1
• Mikail Et
• 1
1. 1.Department of MathematicsFırat UniversityElazigTurkey