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Abel summability of sequences of fuzzy numbers

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Abstract

In the present study, we have introduced the concept of Abel summability for sequences and series of fuzzy numbers. Also, some tauberian results in classical analysis have been generalized to fuzzy analysis.

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References

  • Altın Y, Mursaleen M, Altınok H (2010) Statistical summability \((C; 1)\)-for sequences of fuzzy real numbers and a Tauberian theorem. J Intell Fuzzy Syst 21:379–384

  • Altınok H, Çolak R, Altın Y (2012) On the class of \(\lambda \)-statistically convergent difference sequences of fuzzy numbers. Soft Comput 16(6):1029–1034

    Article  MATH  Google Scholar 

  • Anastassiou GA, Gal SG (2001) On a fuzzy trigonometric approximation theorem of Weierstrass-type. J Fuzzy Math 9(3):701–708

    MathSciNet  MATH  Google Scholar 

  • Bede B, Gal SG (2004) Almost periodic fuzzy-number-valued functions. Fuzzy Sets Syst 147:385–403

    Article  MathSciNet  MATH  Google Scholar 

  • Çanak İ (2014) On the Riesz mean of sequences of fuzzy real numbers. J Intell Fuzzy Syst 26(6):2685–2688

    MATH  Google Scholar 

  • Çanak İ (2014) Tauberian theorems for Cesàro summability of sequences of fuzzy number. J Intell Fuzzy Syst 27(2):937–942

    MATH  Google Scholar 

  • Çolak R, Altın Y, Mursaleen M (2011) On some sets of difference sequences of fuzzy numbers. Soft Comput 15(4):787–793

    Article  MATH  Google Scholar 

  • Diamond P, Kloeden P (1990) Metric spaces of fuzzy sets. Fuzzy Sets Syst 35:241–249

    Article  MathSciNet  MATH  Google Scholar 

  • Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31–43

    Article  MathSciNet  MATH  Google Scholar 

  • Kadak U, Başar F (2012) Power series of fuzzy numbers with real or fuzzy coefficients. Filomat 26(3):519–528

    Article  MathSciNet  MATH  Google Scholar 

  • Kim YK, Ghil BM (1997) Integrals of fuzzy-number-valued functions. Fuzzy Sets Syst 86:213–222

    Article  MathSciNet  MATH  Google Scholar 

  • Matloka M (1986) Sequences of fuzzy numbers. Busefal 28:28–37

    MATH  Google Scholar 

  • Nanda S (1989) On sequence of fuzzy numbers. Fuzzy Sets Syst 33:123–126

    Article  MathSciNet  MATH  Google Scholar 

  • Savaş E (2012) A note on double lacunary statistical \(\sigma \)-convergence of fuzzy numbers. Soft Comput 16(4):591–595

    Article  MATH  Google Scholar 

  • Stojaković M, Stojaković Z (1996) Addition and series of fuzzy sets. Fuzzy Sets Syst 83:341–346

  • Stojaković M, Stojaković Z (2009) Series of fuzzy sets. Fuzzy Sets Syst 160:3115–3127

  • Subrahmanyam PV (1999) Cesàro summability of fuzzy real numbers. J Anal 7:159–168

    MathSciNet  MATH  Google Scholar 

  • Talo Ö, Başar F (2009) Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations. Comput Math Appl 58(4):717–733

    Article  MathSciNet  MATH  Google Scholar 

  • Talo Ö, Çakan C (2012) On the Cesàro convergence of sequences of fuzzy numbers. Appl Math Lett 25:676–681

    Article  MathSciNet  MATH  Google Scholar 

  • Talo Ö, Başar F (2013) On the slowly decreasing sequences of fuzzy numbers. Abstr Appl Anal Article ID 891986 2013, p 1–7. doi:10.1155/2013/891986

  • Tripathy BC, Baruah A (2010) Nörlund and Riesz mean of sequences of fuzzy real numbers. Appl Math Lett 23:651–655

    Article  MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Dutta AJ (2013) Lacunary bounded variation sequence of fuzzy real numbers. J Intell Fuzzy Syst 24(1):185–189

    MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Sen M (2013) On fuzzy I-convergent difference sequence space. J Intell Fuzzy Syst 25(3):643–647

    MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:29–44

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The authors would like to express their pleasure to referees for many helpful suggestions on the main results of the earlier version of the paper which improved the presentation of the paper.

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Correspondence to Özer Talo.

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Communicated by V. Loia.

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Yavuz, E., Talo, Ö. Abel summability of sequences of fuzzy numbers. Soft Comput 20, 1041–1046 (2016). https://doi.org/10.1007/s00500-014-1563-7

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  • DOI: https://doi.org/10.1007/s00500-014-1563-7

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