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On the class of λ-statistically convergent difference sequences of fuzzy numbers

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Abstract

In this study, we introduce the sets \(\left[ V,\lambda ,p\right] _{\Updelta }^{{\mathcal{F}}},\left[ C,1,p\right] _{\Updelta }^{{\mathcal{F}}}\) and examine their relations with the classes of \( S_{\lambda }\left( \Updelta ,{\mathcal{F}}\right)\) and \( S_{\mu }\left( \Updelta ,{\mathcal{F}}\right)\) of sequences for the sequences \(\left( \lambda _{n}\right)\) and \(\left( \mu _{n}\right) , 0<p<\infty \) and difference sequences of fuzzy numbers.

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References

  • Altinok H, Çolak R, Et M (2009) λ-Difference sequence spaces of fuzzy numbers. Fuzzy Sets Syst 160(21):3128–3139

    Article  MATH  Google Scholar 

  • Aytar S, Pehlivan S (2007) Statistically convergence of sequences of fuzzy numbers and sequences of α-cuts. Int J Gen Syst 1–7

  • Başar F, Altay B (2003) On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math J 55(1):136–147

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Çolak R (2011) On λ-statistical convergence. Conference on summability and applications, Commerce University, May 12–13, 2011, Istanbul, Turkey

  • Connor JS (1988) The statistical and strong p-Cesaro convergence of sequences. Analysis 8:47–63

    MathSciNet  MATH  Google Scholar 

  • Diamond P, Kloeden P (1990) Metric spaces of fuzzy sets. Fuzzy Sets Syst 35(2):241–249

    Article  MathSciNet  MATH  Google Scholar 

  • Et M, Çolak R (1995) On some generalized difference sequence spaces. Soochow J Math 21(4):377–386

    MathSciNet  MATH  Google Scholar 

  • Et M, Altin Y, Choudhary B, Tripathy BC (2006) On some classes of sequences defined by sequences of Orlicz functions. Math Inequal Appl 9(2):335–342

    Article  MathSciNet  MATH  Google Scholar 

  • Fast H (1951) Sur la convergence statistique. Colloq Math 2:241–244

    MathSciNet  MATH  Google Scholar 

  • Fridy J (1985) On statistical convergence. Analysis 5:301–313

    MathSciNet  MATH  Google Scholar 

  • Kızmaz H (1985) On certain sequence spaces. Can Math Bull 24(2):169–176

    Article  Google Scholar 

  • Kwon JS (2000) On statistical and p-Cesàro convergence of fuzzy numbers. Korean J Comput Appl Math 7(1):195–203

    MathSciNet  MATH  Google Scholar 

  • Leindler L (1965) Über die de la Vallée-Pousinsche Summierbarkeit allgemeiner Orthogonalreihen. Acta Math Acad Sci Hungar 16:375–387

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Mursaleen M (2000) λ-Statistical convergence. Math Slovaca 50(1):111–115

    MathSciNet  MATH  Google Scholar 

  • Nuray F, Savaş E (1995) Statistical convergence of sequences of fuzzy real numbers. Math Slovaca 45(3):269–273

    MathSciNet  MATH  Google Scholar 

  • Šalát T (1980) On statistically convergent sequences of real numbers. Math Slovaca 30:139–150

    MathSciNet  MATH  Google Scholar 

  • Savaş E (2000) Strong almost convergence and almost λ-statistical convergence. Hokkaido Math J 29(3):531–536

    MathSciNet  MATH  Google Scholar 

  • Schoenberg IJ (1959) The integrability of certain functions and related summability methods. Am Math Monthly 66:361–375

    Article  MathSciNet  MATH  Google Scholar 

  • Steinhaus H (1951) Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum 2:73–74

    MathSciNet  Google Scholar 

  • Tripathy BC (2004) On generalized difference paranormed statistically convergent sequences. Indian J Pure Appl Math 35(5):655–663

    MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Baruah A (2010a) N örlund and Riesz mean of sequences of fuzzy real numbers. Appl Math Lett 23(5):651–655

    Article  MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Baruah A (2010b) Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers. Kyungpook Math J 50:565–574

    MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Chandra P (2011) On some generalized difference paranormed sequence spaces associated with multiplier sequences defined by modulus function. Anal Theory Appl 27(1):21–27

    Article  MathSciNet  Google Scholar 

  • Tripathy BC, Dutta AJ (2007) On fuzzy real-valued double sequence spaces \(_{2}l_{{\mathcal{F}}}^{p}\). Math Comput Model 46(9–10):1294–1299

    Google Scholar 

  • Tripathy BC, Sarma B (2008) Sequences spaces of fuzzy real numbers defined by Orlicz functions. Math Slovaca 58(5):621–628

    Article  MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Altin Y, Et M (2008a) Generalized difference sequences spaces on seminormed spaces defined by Orlicz functions. Math Slovaca 58(3):315–324

    Article  MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Choudhary B, Sarma B (2008b) On some new type generalized differences sequence spaces. Kyungpook Math J 48(4):613–622

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Firat University, 23119, Elazig, Turkey

    Hifsi Altinok, Rifat Çolak & Yavuz Altin

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  1. Hifsi Altinok
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  2. Rifat Çolak
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  3. Yavuz Altin
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Correspondence to Yavuz Altin.

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Altinok, H., Çolak, R. & Altin, Y. On the class of λ-statistically convergent difference sequences of fuzzy numbers. Soft Comput 16, 1029–1034 (2012). https://doi.org/10.1007/s00500-011-0800-6

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