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

  • Hifsi Altinok
  • Mikail Et
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 

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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Copyright information

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

Authors and Affiliations

  1. 1.Department of MathematicsFırat UniversityElazigTurkey

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