Statistical Riesz and Nörlund convergence for sequences of fuzzy numbers

Yıl 2023, Cilt: 4 Sayı: 2, 100 - 107, 31.12.2023

Burak Arslan , Samira Jalali , Serdar Enginoğlu

https://doi.org/10.54559/jauist.1400386

Öz

Nuray and Savaş proposed statistical convergence of fuzzy number sequences. Afterward, Tripathy and Baruah presented Riesz and Nörlund convergence for sequences of fuzzy numbers. This paper defines statistical Riesz and Nörlund convergence of fuzzy number sequences. It then shows that if a sequence of fuzzy numbers is convergent, then it is statistical Riesz/Nörlund convergent, but the converse is not always true. Finally, this paper discusses the need for further research.

Anahtar Kelimeler

Statistical convergence, statistical Riesz convergence, statistical Nörlund convergence, sequences of fuzzy numbers

Kaynakça

• V. Loku, N. L. Braha, M. Et, A. Tato, Tauberian theorems for the generalized de la Vallée-Poussin mean-convergent sequences of fuzzy numbers, Bulletin of Mathematical Analysis and Applications 9 (2) (2017) 45–56.
• S. Enginoğlu, S. Demiriz, A comparison with the convergent, Cesàro convergent and Riesz convergent sequences of fuzzy numbers, in: İ. Yüksek, F. Yiğit, H. Baraçlı (Eds.), FUZZYSS’15 The 4th International Fuzzy Systems Symposium, İstanbul, 2015, pp. 416–419.
• B. C. Tripathy, A. Baruah, Nörlund and Riesz mean of sequences of fuzzy real numbers, Applied Mathematics Letters 23 (5) (2010) 651–655.
• M. Matloka, Sequences of fuzzy numbers, BUSEFAL 28 (1) (1986) 28–37.
• S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems 33 (1) (1989) 123–126.
• F. Nuray, E. Savaş, Statistical convergence of sequences of fuzzy numbers, Mathematica Slovaca 45 (3) (1995) 269–273.
• J-S. Kwon, On statistical and p-Cesàro convergence of fuzzy numbers, Korean Journal of Computational and Applied Mathematics 7 (1) (2000) 195–203.
• Y. Altın, M. Mursaleen, H. Altınok, Statistical summability (C,1) for sequences of fuzzy real numbers and a Tauberian theorem, Journal of Intelligent & Fuzzy Systems 21 (6) (2010) 379–858.
• S. Aytar, S. Pehlivan, Statistical convergence of sequences of fuzzy numbers and sequences of α-cuts, International Journal of General Systems 37 (2) (2008) 231–237.