Year 2020,
Volume: 8 Issue: 1, 62 - 69, 15.04.2020
Özer Talo
Enes Yavuz
,
Hüsamettin Çoşkun
References
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976–985.
- [2] S. Aytar and S. Pehlivan, Statistical cluster and extreme limit points of sequences of fuzzy numbers, Inform. Sci. 177, No. 16 (2007) 3290–3296
- [3] B. Bede and S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Set Syst 147, (2004) 385–403.
- [4] C. Belen, Tauberian theorems for weighted mean summability method of improper Riemann integrals of fuzzy-number-valued functions, Soft Comput 22,
No. 12 (2018) 3951–3957
- [5] C. Belen, Tauberian theorems for statistical limit and statistical summability by weighted means of continuous fuzzy valued functions, J. Math. Ext.
(2020), preprint
- [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2, (1951) 241–244.
- [7] O. Kaleva, Fuzzy differential equations, Fuzzy Set Syst 24, (1987) 301–317.
- [8] Y. K. Kim and B. M. Ghil, Integrals of fuzzy-number-valued functions, Fuzzy Set Syst 86, (1997) 213–222
- [9] H. Li and C. Wu, The integral of a fuzzy mapping over a directed line, Fuzzy Set Syst 158, (2007) 2317–2338.
- [10] J. Li, A. Zhao and J. Yan, The Cauchy problem of fuzzy differential equations under generalized differentiability, Fuzzy Set Syst 200, (2012) 1–24.
- [11] F. Moricz, Statistical limits of measurable functions, Analysis 24, (2004) 1–18.
- [12] F. Moricz, Statistical extensions of some classical Tauberian theorems in nondiscrete setting, Colloq. Math. 107, No. 1 (2007) 45–56.
- [13] F. Moricz and Nemeth Z., Statistical extension of classical Tauberian theorems in the case of logarithmic summability, Anal. Math. 40, No. 3 (2014)
231–242.
- [14] O. Talo and F. Basar, On the Slowly Decreasing Sequences of Fuzzy Numbers, Abstr. Appl. Anal. 2013, (2013) 1–7.
- [15] E. Yavuz, O. Talo and H. C¸ os¸kun, Cesa`ro summability of integrals of fuzzy-number-valued functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
67, No. 2 (2018) 38–49.
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On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions
Year 2020,
Volume: 8 Issue: 1, 62 - 69, 15.04.2020
Özer Talo
Enes Yavuz
,
Hüsamettin Çoşkun
Abstract
We introduce the notions of statistical limit, statistical Cesaro summability of strongly measurable fuzzy valued functions and give slowly decreasing-slowly oscillating type Tauberian conditions under which statistical limits and statistical Cesaro summability of fuzzy valued functions imply ordinary limits in fuzzy number space.
References
- [1] S. Aytar, M. Mammadov and S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Set Syst 157, No. 7 (2006)
976–985.
- [2] S. Aytar and S. Pehlivan, Statistical cluster and extreme limit points of sequences of fuzzy numbers, Inform. Sci. 177, No. 16 (2007) 3290–3296
- [3] B. Bede and S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Set Syst 147, (2004) 385–403.
- [4] C. Belen, Tauberian theorems for weighted mean summability method of improper Riemann integrals of fuzzy-number-valued functions, Soft Comput 22,
No. 12 (2018) 3951–3957
- [5] C. Belen, Tauberian theorems for statistical limit and statistical summability by weighted means of continuous fuzzy valued functions, J. Math. Ext.
(2020), preprint
- [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2, (1951) 241–244.
- [7] O. Kaleva, Fuzzy differential equations, Fuzzy Set Syst 24, (1987) 301–317.
- [8] Y. K. Kim and B. M. Ghil, Integrals of fuzzy-number-valued functions, Fuzzy Set Syst 86, (1997) 213–222
- [9] H. Li and C. Wu, The integral of a fuzzy mapping over a directed line, Fuzzy Set Syst 158, (2007) 2317–2338.
- [10] J. Li, A. Zhao and J. Yan, The Cauchy problem of fuzzy differential equations under generalized differentiability, Fuzzy Set Syst 200, (2012) 1–24.
- [11] F. Moricz, Statistical limits of measurable functions, Analysis 24, (2004) 1–18.
- [12] F. Moricz, Statistical extensions of some classical Tauberian theorems in nondiscrete setting, Colloq. Math. 107, No. 1 (2007) 45–56.
- [13] F. Moricz and Nemeth Z., Statistical extension of classical Tauberian theorems in the case of logarithmic summability, Anal. Math. 40, No. 3 (2014)
231–242.
- [14] O. Talo and F. Basar, On the Slowly Decreasing Sequences of Fuzzy Numbers, Abstr. Appl. Anal. 2013, (2013) 1–7.
- [15] E. Yavuz, O. Talo and H. C¸ os¸kun, Cesa`ro summability of integrals of fuzzy-number-valued functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
67, No. 2 (2018) 38–49.
- [16] L. A. Zadeh, Fuzzy sets, Inform. Control 8, (1965) 338–353.