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Year 2020, Volume: 8 Issue: 1, 62 - 69, 15.04.2020

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

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 Articles
Authors

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

Enes Yavuz 0000-0002-4335-5210

Hüsamettin Çoşkun 0000-0002-2344-9682

Publication Date April 15, 2020
Submission Date May 19, 2019
Acceptance Date March 28, 2020
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.
AMA Talo Ö, Yavuz E, Çoşkun H. On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp J. Math. April 2020;8(1):62-69.
Chicago Talo, Özer, Enes Yavuz, and Hüsamettin Çoşkun. “On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 62-69.
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 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, 2020.
ISNAD Talo, Özer et al. “On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions”. Konuralp Journal of Mathematics 8/1 (April 2020), 62-69.
JAMA 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, 2020, pp. 62-69.
Vancouver Talo Ö, Yavuz E, Çoşkun H. On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions. Konuralp J. Math. 2020;8(1):62-9.
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