Research Article

Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions

Volume: 3 Number: 2 June 30, 2020
Özer Talo , Enes Yavuz *, Husamettin Coşkun
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences
EN

Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions

Abstract

We define statistical logarithmic summability of strongly measurable fuzzy valued functions and we give slowly decreasing type Tauberian conditions under which statistical limit at infinity and statistical logarithmic summability of strongly measurable fuzzy valued functions imply ordinary limit at infinity in one dimensional fuzzy number space $E^1$. Besides, we give slowly oscillating type Tauberian conditions for statistical limit and statistical logarithmic summability of strongly measurable fuzzy valued functions in $n-$dimensional fuzzy number space $E^n$.

Keywords

fuzzy set theory, statistical limits, logarithmic summability, Tauberian theorems

References

  1. [1] L. A. Zadeh, Fuzzy sets, Inform. Control 8(1965) 338–353.
  2. [2] J. Li, A. Zhao and J. Yan, The Cauchy problem of fuzzy differential equations under generalized differentiability, Fuzzy Set Syst 200(2012) 1–24.
  3. [3] O. Kaleva, Fuzzy differential equations, Fuzzy Set Syst 24(1987) 301–317.
  4. [4] S. Aytar, M. Mammadov and S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Set Syst 157(7) (2006) 976–985.
  5. [5] S. Aytar and S. Pehlivan, Statistical cluster and extreme limit points of sequences of fuzzy numbers, Inform. Sci. 177(16) (2007) 3290–3296
  6. [6] H. Li and C. Wu, The integral of a fuzzy mapping over a directed line, Fuzzy Set Syst 158(2007) 2317–2338.
  7. [7] O. Talo and F. Basar, On the slowly decreasing sequences of fuzzy numbers, Abstr. Appl. Anal. 2013(2013) 1–7.
  8. [8] Y. K. Kim and B. M. Ghil, Integrals of fuzzy-number-valued functions, Fuzzy Set Syst 86(1997) 213–222
  9. [9] O. Talo, E. Yavuz and H. Coskun, On the statistical limits of strongly measurable fuzzy valued functions, Konuralp Journal of Mathematics 8(1) (2020), 62–69
  10. [10] C. Belen, Tauberian theorems for statistical limit and statistical summability by weighted means of continuous fuzzy valued functions, J. Math. Ext. 14(4) (2020)

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Özer Talo This is me
Türkiye

Publication Date

June 30, 2020

Submission Date

April 26, 2020

Acceptance Date

June 15, 2020

Published in Issue

Year 2020 Volume: 3 Number: 2

DOI

https://doi.org/10.33434/cams.727129

IZ

https://izlik.org/JA99NB47WM

Cite

RIS / Bibtex
APA
Talo, Ö., Yavuz, E., & Coşkun, H. (2020). Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions. Communications in Advanced Mathematical Sciences, 3(2), 91-100. https://doi.org/10.33434/cams.727129
AMA
1.Talo Ö, Yavuz E, Coşkun H. Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions. Communications in Advanced Mathematical Sciences. 2020;3(2):91-100. doi:10.33434/cams.727129
Chicago
Talo, Özer, Enes Yavuz, and Husamettin Coşkun. 2020. “Tauberian Theorems for Statistical Logarithmic Summability of Strongly Measurable Fuzzy Valued Functions”. Communications in Advanced Mathematical Sciences 3 (2): 91-100. https://doi.org/10.33434/cams.727129.
EndNote
Talo Ö, Yavuz E, Coşkun H (June 1, 2020) Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions. Communications in Advanced Mathematical Sciences 3 2 91–100.
IEEE
[1]Ö. Talo, E. Yavuz, and H. Coşkun, “Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions”, Communications in Advanced Mathematical Sciences, vol. 3, no. 2, pp. 91–100, June 2020, doi: 10.33434/cams.727129.
ISNAD
Talo, Özer - Yavuz, Enes - Coşkun, Husamettin. “Tauberian Theorems for Statistical Logarithmic Summability of Strongly Measurable Fuzzy Valued Functions”. Communications in Advanced Mathematical Sciences 3/2 (June 1, 2020): 91-100. https://doi.org/10.33434/cams.727129.
JAMA
1.Talo Ö, Yavuz E, Coşkun H. Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions. Communications in Advanced Mathematical Sciences. 2020;3:91–100.
MLA
Talo, Özer, et al. “Tauberian Theorems for Statistical Logarithmic Summability of Strongly Measurable Fuzzy Valued Functions”. Communications in Advanced Mathematical Sciences, vol. 3, no. 2, June 2020, pp. 91-100, doi:10.33434/cams.727129.
Vancouver
1.Özer Talo, Enes Yavuz, Husamettin Coşkun. Tauberian theorems for statistical logarithmic summability of strongly measurable fuzzy valued functions. Communications in Advanced Mathematical Sciences. 2020 Jun. 1;3(2):91-100. doi:10.33434/cams.727129

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