Skip to main content
Springer Nature Link
Log in

On the logarithmic summability method for sequences of fuzzy numbers

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

We define logarithmic summability method for sequences of fuzzy numbers and prove theorems dealing with the convergence behavior of logarithmic summable sequences of fuzzy numbers. The study also reveals slowly decreasing and Landau one-sided type Tauberian results analogous to those given by Móricz (Stud Math 219:109–121, 2013).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Alghamdi MA, Mursaleen M, Alotaibi A (2013) Logarithmic density and logarithmic statistical convergence. Adv Differ Eq 227:1–6

    MathSciNet  Google Scholar 

  • 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 

  • Aytar S, Mammadov M, Pehlivan S (2006) Statistical limit inferior and limit superior for sequences of fuzzy numbers. Fuzzy Sets Syst 157(7):976–985

    Article  MathSciNet  MATH  Google Scholar 

  • Aytar S, Pehlivan S (2007) Statistical cluster and extreme limit points of sequences of fuzzy numbers. Inf Sci 177(16):3290–3296

    Article  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 

  • Chishti TA (2013) Some Inequalities on class of matrices and statistical harmonic summability. Int J Eng Math Sci 4(1):1–7

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Çanak İ (2014) Hölder summability method of fuzzy numbers and a Tauberian theorem. Iran J Fuzzy Syst 11(4):87–93

    MathSciNet  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 

  • Getsadze R (2011) On the strong logarithmic summability of the double trigonometric Fourier series. Acta Sci Math 77:473–488

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Li H, Wu C (2007) The integral of a fuzzy mapping over a directed line. Fuzzy Sets Syt 158:2317–2338

    Article  MathSciNet  MATH  Google Scholar 

  • Móricz F (2004) Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences. Analysis 24:127–145

    MathSciNet  MATH  Google Scholar 

  • Móricz F (2006) On the harmonic averages of numerical sequences. Archiv der Math 86:375–384

    Article  MathSciNet  MATH  Google Scholar 

  • Móricz F (2013) Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences. Stud Math 219:109–121

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Srivastava PD, Ojha S (2014) \(\lambda \)-Statistical convergence of fuzzy numbers and fuzzy functions of order \(\theta \). Soft Comput 18(5):1027–1032

    Article  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. Abstract and Applied Analysis, pp 1–7. doi:10.1155/2013/891986 (Article ID 891986)

  • Talo Ö, Çakan C (2014) Tauberian theorems for statistically \((C; 1)-\)convergent sequences of fuzzy numbers. Filomat 28:849–858

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • Yavuz E, Talo Ö (2016) Abel summability of sequences of fuzzy numbers. Soft Comput 20(3):1041–1046

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Letters, Celal Bayar University, Manisa, Turkey

    Enes Yavuz & Hüsamettin Çoşkun

Authors
  1. Enes Yavuz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hüsamettin Çoşkun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hüsamettin Çoşkun.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yavuz, E., Çoşkun, H. On the logarithmic summability method for sequences of fuzzy numbers. Soft Comput 21, 5779–5785 (2017). https://doi.org/10.1007/s00500-016-2156-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2156-4

Keywords

Search

Navigation