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Year 2020, Volume: 8 Issue: 1, 62 - 69, 15.04.2020
https://izlik.org/JA42ZF85JH

Abstract

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.

On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions

Year 2020, Volume: 8 Issue: 1, 62 - 69, 15.04.2020
https://izlik.org/JA42ZF85JH

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.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Özer Talo This is me 0000-0003-1393-5414

Enes Yavuz 0000-0002-4335-5210

Hüsamettin Çoşkun 0000-0002-2344-9682

Submission Date May 19, 2019
Acceptance Date March 28, 2020
Publication Date April 15, 2020
IZ https://izlik.org/JA42ZF85JH
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Talo, Ö., Yavuz, E., & Çoşkun, H. (2020). On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp Journal of Mathematics, 8(1), 62-69. https://izlik.org/JA42ZF85JH
AMA 1.Talo Ö, Yavuz E, Çoşkun H. On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp J. Math. 2020;8(1):62-69. https://izlik.org/JA42ZF85JH
Chicago Talo, Özer, Enes Yavuz, and Hüsamettin Çoşkun. 2020. “On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions”. Konuralp Journal of Mathematics 8 (1): 62-69. https://izlik.org/JA42ZF85JH.
EndNote Talo Ö, Yavuz E, Çoşkun H (April 1, 2020) On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp Journal of Mathematics 8 1 62–69.
IEEE [1]Ö. Talo, E. Yavuz, and H. Çoşkun, “On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions”, Konuralp J. Math., vol. 8, no. 1, pp. 62–69, Apr. 2020, [Online]. Available: https://izlik.org/JA42ZF85JH
ISNAD Talo, Özer - Yavuz, Enes - Çoşkun, Hüsamettin. “On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions”. Konuralp Journal of Mathematics 8/1 (April 1, 2020): 62-69. https://izlik.org/JA42ZF85JH.
JAMA 1.Talo Ö, Yavuz E, Çoşkun H. On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp J. Math. 2020;8:62–69.
MLA Talo, Özer, et al. “On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions”. Konuralp Journal of Mathematics, vol. 8, no. 1, Apr. 2020, pp. 62-69, https://izlik.org/JA42ZF85JH.
Vancouver 1.Özer Talo, Enes Yavuz, Hüsamettin Çoşkun. On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp J. Math. [Internet]. 2020 Apr. 1;8(1):62-9. Available from: https://izlik.org/JA42ZF85JH
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