Title of paper:
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On λ-statistical convergence of order α in intuitionistic fuzzy normed spaces
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Author(s):
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Ekrem Savaş
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Department of Mathematics, Istanbul Commerce University, Sutluce-Istanbul, Turkey
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ekremsavas@yahoo.com
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Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 4, pages 13–22
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Download:
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PDF (199 Kb, File info)
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Abstract:
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The purpose of this paper is to introduce the notion [V, λ] (ℐ)-summability and ℐλ-statistical convergence of order α with respect to the intuitionistic fuzzy norm (μ, ν), investigate
their relationship, and make some observations about these classes. We also study the relation between ℐλ-statistical convergence of order α and ℐ-statistical convergence of order α in intuitionistic fuzzy normed space (μ, ν).
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Keywords:
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Ideal, Filter, ℐ-statistical convergence, ℐλ-statistical convergence order α, ℐ-[V, λ]-summability, Closed subspace.
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AMS Classification:
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40G99.
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References:
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- Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
- K. Atanassov, G. Pasi & R. Yager (2002) Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, Proc. of 1st Int. IEEE Symp. Intelligent Systems, 1, 115–119.
- Cakalli, H. (2009) A study on statistical convergence, Funct. Anal. Approx. Comput., 1(2), 19–24, MR2662887.
- Colak, R. (2010) Statistical convergence of order α, Modern methods in Analysis and Its Applications, New Delhi, India, Anamaya Pub., 121–129.
- Colak, R. & C. A. Bektas (2011) λ-statistical convergence of order α, Acta Math. Scientia, 31B(3), 953–959.
- Das, P. & S. (2010) Ghosal, Some further results on ℐ-Cauchy sequences and condition (AP), Comput. Math. Appl., 59, 2597–2600.
- Das, P., E. Savaş & S. Kr. Ghosal (2011) On generalizations of certain summability methods using ideals, Appl. Math. Lett., 24(2011), 1509–1514.
- Fast, H. (1951) Sur la convergence statistique, Colloq. Math., 2(1951), 241–244.
- Fridy, J. A. (1985) On statistical convergence, Analysis, 5, 301–313.
- Karakus, S., K. Demirci, & O. Duman (2008) Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals 35, 763–769.
- Kostyrko, P., T. Šalát & W. Wilczynki (2000–2001) ℐ-convergence, Real Anal. Exchange, 26(2), 669–685.
- Maio, G. D. & L. D. R. Kocinac (2008) Statistical convergence in topology, Topology Appl., 156, 28–45.
- Maddox, I. J. (1979) On strong almost convergence. Math. Proc. Cambridge Philos. Soc., 85(2), 345–350.
- Malkowsky, E. & E. Savas¸ (2000) Some λ-sequence spaces defined by a modulus. Arch.Math. (Brno), 36(3), 219–228.
- Mursaleen, M. (2000) λ-statistical convergence, Math. Slovaca, 50, 111–115.
- Mohiuddine, S. A. & Q. M. Danish Lohani (2009) On generalized statistical convergence in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 42, 1731–1737.
- Mursaleen, M., S. A. Mohiuddine & H. H. Edely (2010) On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59, 603–611.
- Park, J. H. (2004) Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22, 1039–1046.
- Saadati, R. & J. H. Park (2006) On the intuitioistic fuzzy topologicial spaces, Chaos Solitons Fractals, 27, 331–344.
- Šalát, T. (1980) On statistically convergent sequences of real numbers, Math. Slovaca, 30, 139–150.
- Savaş, E., P. Das (2011) A generalized statistical convergence via ideals, Appl. Math. Lett., 24, 826–830.
- Savaş, E. (2010) Δm-strongly summable sequences spaces in 2-Normed Spaces defined by Ideal Convergence and an Orlicz Function, App. Math. Comp., 217, 271–276.
- Savaş, E. (2011) A-sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function, Abst. Appl. Anal., Vol. 2011, Article ID 741382.
- Savaş, E. (2010) On some new sequence spaces in 2-normed spaces using Ideal convergence and an Orlicz function, J. Ineq. Appl., Article Number: 482392 DOI: 10.1155/2010/482392.
- Savaş, E. (2012) On generalized double statistical convergence via ideals, The Fifth Saudi Science Conference, 16–18 April 2012.
- Savaş, E. (2012) Some double lacunary ℐ-convergent sequence spaces of fuzzy numbers defined by Orlicz function, Journal of Intelligent & Fuzzy Systems, 23, 249–257.
- Savaş, E. (2015) Generalized statistical convergence in intuitionistic fuzzy 2-normed space. Appl. Math. Inf. Sci., 9(1L), 59–63, 40A35.
- Savaş, E. & M. Gurdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces (in press).
- Schoenberg, I. J. (1959) The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, 361–375.
- Schweizer, B. & A. Sklar (1960) Statistical metric spaces, Pacific J. Math., 10, 313–334.
- Zadeh, L. A. (1965) Fuzzy sets, Inform. Control, 8, 338–353.
- Zygmund, A. (1979) Trigonometric Series, Cambridge, UK, Cambridge University Press.
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