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Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers

Year 2019, Volume: 7 Issue: 1, 66 - 74, 01.01.2019

Abstract

We introduce (C,k) summability method of sequences of fuzzy numbers and compare (C,k) summability method with Abel summability method, Hölder summability method and with higher order Cesàro method of sequences of fuzzy numbers. Some Tauberian conditions under which (C,k) summability of sequences of fuzzy numbers imply convergence in fuzzy number space are also obtained as corollaries.

References

  • Zadeh LA. Fuzzy sets. Inf Control 1965; 8: 29-44.
  • Nanda S. On sequence of fuzzy numbers. Fuzzy Sets Syst 1989; 33: 123-126.
  • Jiqing Q, Congxin W, Fachao L. On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets Syst 2000; 115(3): 445-450.
  • Fang J, Huang H. On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets Syst 2004 147(3); 417-435.
  • [5] Stojaković M, Stojaković Z. Series of fuzzy sets. Fuzzy Sets Syst 2009; 160(21): 3115-3127.
  • Altın Y, Mursaleen M, Altınok H. Statistical summability for sequences of fuzzy real numbers and a Tauberian theorem. J Intell Fuzzy Syst 2010; 21: 379-384.
  • Dutta H. A new class of strongly summable and statistical convergence sequences of fuzzy numbers. Appl Math Inf Sci 2013; 7(6): 2369-2372.
  • Talo Ö, Bal C. On statistical summability of sequences of fuzzy numbers. Filomat 2016; 30(3): 873-884.
  • Bede B, Gal SG. Almost periodic fuzzy-number-valued functions. Fuzzy Sets Syst 2004; 147: 385-403.
  • Kim YK, Ghil BM. Integrals of fuzzy-number-valued functions. Fuzzy Sets Syst 1997; 86: 213-222.
  • Yavuz E. Euler summability method of sequences of fuzzy numbers and a Tauberian theorem. J Intell Fuzzy Syst 2017; 32(1): 937-943.
  • Yavuz E. Comparison theorems for summability methods of sequences of fuzzy numbers. J Intell Fuzzy Syst 2018; 35(1): 651-658.
  • Talo Ö, Başar F., Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations. Comput Math Appl 2009; 58(4): 717-733.
  • Çanak İ. Hölder summability method of fuzzy numbers and a Tauberian theorem. Iran J Fuzzy Syst 2014; 11(4): 87-93.
  • Yavuz E. Tauberian theorems for statistical summability methods of sequences of fuzzy numbers. Soft Comput 2018; doi: 10.1007/s00500-018-3222-x
  • Sezer SA, Çanak İ. Power series methods of summability for series of fuzzy numbers and related Tauberian Theorems. Soft Comput 2017; 21(4): 1057-1064.
Year 2019, Volume: 7 Issue: 1, 66 - 74, 01.01.2019

Abstract

References

  • Zadeh LA. Fuzzy sets. Inf Control 1965; 8: 29-44.
  • Nanda S. On sequence of fuzzy numbers. Fuzzy Sets Syst 1989; 33: 123-126.
  • Jiqing Q, Congxin W, Fachao L. On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets Syst 2000; 115(3): 445-450.
  • Fang J, Huang H. On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets Syst 2004 147(3); 417-435.
  • [5] Stojaković M, Stojaković Z. Series of fuzzy sets. Fuzzy Sets Syst 2009; 160(21): 3115-3127.
  • Altın Y, Mursaleen M, Altınok H. Statistical summability for sequences of fuzzy real numbers and a Tauberian theorem. J Intell Fuzzy Syst 2010; 21: 379-384.
  • Dutta H. A new class of strongly summable and statistical convergence sequences of fuzzy numbers. Appl Math Inf Sci 2013; 7(6): 2369-2372.
  • Talo Ö, Bal C. On statistical summability of sequences of fuzzy numbers. Filomat 2016; 30(3): 873-884.
  • Bede B, Gal SG. Almost periodic fuzzy-number-valued functions. Fuzzy Sets Syst 2004; 147: 385-403.
  • Kim YK, Ghil BM. Integrals of fuzzy-number-valued functions. Fuzzy Sets Syst 1997; 86: 213-222.
  • Yavuz E. Euler summability method of sequences of fuzzy numbers and a Tauberian theorem. J Intell Fuzzy Syst 2017; 32(1): 937-943.
  • Yavuz E. Comparison theorems for summability methods of sequences of fuzzy numbers. J Intell Fuzzy Syst 2018; 35(1): 651-658.
  • Talo Ö, Başar F., Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations. Comput Math Appl 2009; 58(4): 717-733.
  • Çanak İ. Hölder summability method of fuzzy numbers and a Tauberian theorem. Iran J Fuzzy Syst 2014; 11(4): 87-93.
  • Yavuz E. Tauberian theorems for statistical summability methods of sequences of fuzzy numbers. Soft Comput 2018; doi: 10.1007/s00500-018-3222-x
  • Sezer SA, Çanak İ. Power series methods of summability for series of fuzzy numbers and related Tauberian Theorems. Soft Comput 2017; 21(4): 1057-1064.
There are 16 citations in total.

Details

Journal Section Articles
Authors

Enes Yavuz

Publication Date January 1, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Yavuz, E. (2019). Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 7(1), 66-74.
AMA Yavuz E. Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. January 2019;7(1):66-74.
Chicago Yavuz, Enes. “Inclusion Theorems for (C,k) Summability Method of Sequences of Fuzzy Numbers”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 7, no. 1 (January 2019): 66-74.
EndNote Yavuz E (January 1, 2019) Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 7 1 66–74.
IEEE E. Yavuz, “Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 7, no. 1, pp. 66–74, 2019.
ISNAD Yavuz, Enes. “Inclusion Theorems for (C,k) Summability Method of Sequences of Fuzzy Numbers”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 7/1 (January 2019), 66-74.
JAMA Yavuz E. Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2019;7:66–74.
MLA Yavuz, Enes. “Inclusion Theorems for (C,k) Summability Method of Sequences of Fuzzy Numbers”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 7, no. 1, 2019, pp. 66-74.
Vancouver Yavuz E. Inclusion theorems for (C,k) summability method of sequences of fuzzy numbers. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2019;7(1):66-74.