On I-lacunary Summability Methods of Order a in Intuitionistic Fuzzy n-normed Spaces
DOI:
https://doi.org/10.5890/DNC.2018.12.001Abstract
In this paper we introduce and study the notion I-statistical convergence of order α, and I-lacunary statistical convergence of order a with respect to the intuitionistic fuzzy n-normed space and also we investigate their relationship and some inclusion theorems are roved.References
[1] Zadeh, L.A. (1965), Fuzzy sets, Inform. Control, 8(1965), 338-353.
[2] Nanda, S. (1989), On sequences of fuzzy numbers, Fuzzy Sets and Systems, 33, 123-126.
[3] Nuray, F. and Savaş, E. (1994) Statistical convergence of sequences of fuzzy numbers, Math. Slovaca, 99(3), 353-355.
[4] Tripathy, B.C. and Dutta, A.J. (2010), Bounded variation double sequence space of fuzzy real numbers, Computers and Mathematics with Applications, 59, 1031-1037.
[5] Tripathy, B.C. and Dutta, A.J. (2013), Lacunary bounded variation sequence of fuzzy real numbers, Journal of Intelligent and fuzzy systems, 24, 185-189.
[6] Atanassov, K.T. (1986), Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96.
[7] Atanassov, K., Pasi, G., and Yager, R. (2002), Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, in: Proceedings of 2002 First International IEEE Symposium Intelligent Systems, 1(2002), 115-119.
[8] Park, J.H. (2004), Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22, 1039-1046.
[9] Saadati, R. and Park, J.H. (2006), On the intuitioistic fuzzy topologicial spaces, Chaos Solitons Fractals, 27, 331-344.
[10] Karakus, S., Demirci, K., and Duman, O. (2008), Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals, 35, 763-769.
[11] Mursaleen, M. and Danish Lohani, Q.M. (2009), Intuitionistic fuzzy 2- normed space and some relates concepts, Chaos, Solitons and Fractals, 42, 224-234.
[12] Savaş, E. (2015), Generalized statistical convergence in intuitionistic fuzzy 2-normed space, Appl. Math. Inf. Sci., 9(1L), 59-63.
[13] Savaş, E. (2015), On λ-statistical convergence of order a in intuitionistic fuzzy normed spaces, second International IFS conference, Mersin Turkey, 14-18 October, 2015. Notes On intuitionistic fuzzy sets, 21(4), 13-22.
[14] Sen, M. and Debnath, P. (2011), Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, Math. Comput. Modelling, 54, 2978-2985.
[15] Fast, H. (1951), Sur la convergence statistique, Colloq. Math., 2, 241-244.
[16] Schoenberg, I.J. (1959), The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, 361-375.
[17] Fridy, J.A. (1985), On statistical convergence, Analysis, 5, 301-313.
[18] Šalát, T. (1980), On statistically convergent sequences of real numbers, Math. Slovaca, 30, 139-150.
[19] Kostyrko, P., Šalát, T., and Wilczynki,W. (2000-2001),I-convergence, Real Anal. Exchange, 26(2), 669-685.
[20] Das, P. and Savaş, E. (2014), On I-statistical and I-lacunary statistical convergence of order alpha, Bull. iranian Soc., 40(2), 459-472.
[21] Das, P., Savaş, E., and Ghosal, S.Kr. (2011), On generalizations of certain summability methods using ideals, Appl. Math. Lett., 24, 1509-1514.
[22] Savaş, E. and Gurdal, M. (2014), Certain summability methods in intuitionistic fuzzy normed spaces, Journal of Intelligent & Fuzzy Systems, 27, 1621-1629.
[23] Savaş, E. and Pratulananda, D. (2011), A generalized statistical convergence via ideals, Appl. Math. Lett., 24, 826-830.
[24] Savaş, E. (2015), On some summability methods using ideals and fuzzy numbers, J. Intell. Fuzzy Systems, 28(4), 1931-1936
[25] Savaş, E. (2013), On generalized I -statistical convergence of order a, Iran. J. Sci. Technol. Trans. A Sci., 37(3), Special issue: Mathematics, 397-402.
[26] Savaş, E. (2013), Some I -convergent sequence spaces of fuzzy numbers defined by infinite matrix, Math. Comput. Appl., 18(2), 84-93.
[27] Savaş, E. (2012), On generalized A - difference strongly summable sequence spaces defined by ideal convergence on a real n -normed space, J. Inequal. Appl., 87, 9.
[28] Savaş, E. (2011), I -lacunary vector valued sequence spaces in 2-normed spaces via Orlicz function, Aligarh Bull. Math., 30(1-2), 25-34.
[29] Savaş, E. and Gurdal,M. (2015), A generalized statistical convergence in intuitionistic fuzzy normed spaces, ScienceAsia, 41, 289-294.
[30] Fridy, J.A. and Orhan, C. (1993), Lacunary statistical convergence, Pacific J. Math., 160, 43-51.
[31] Mohiuddine, S. and Aiyub, A.M. (2012), Lacunary statistical convergence in random 2-normed spaces, Appl. Math. Inf. Sci., 6(3), 581-585.
[32] Mursaleen, M. and Mohiuddine, S.A. (2009), On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233, 142-149.
[33] Mohiuddine, S.A. and Savaş, E. (2012), Lacunary statistically convergent double sequences in probabilistic normed spaces, Ann. Univ. Ferrara, 58, 331-339.
[34] Mursaleen,M., Mohiuddine, S.A., and Edely, H.H. (2010), On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59, 603-611.
[35] Savaş, E. (2015), On I -lacunary statistical convergence of order a for sequences of sets, Filomat, 29(6), 1223-1229.
[36] Bhunia, S., Pratulananda, D., Pal, S. (2012), Restricting statistical convergenge, Acta Math. Hungar, 134(1-2), 153- 161.
[37] Colak, R. (2010), Statistical convergence of order a, Modern methods in Analysis and its Applications, New Delhi, India, Anamaya Pub., 121-129.
[38] Schweizer, B. and Sklar, A. (1960), Statistical metric spaces, Pacific J. Math., 10, 313-334.
[39] Gähler, S. (1965), Lineare 2-normietre räume, Math. Nachr., 28, 1-43.
[40] Gähler, S. (1969), Untersuchungen uber verallgemeinerte m-metrische räume, I, II, III, Math. Nachr., 40, 165-189.
[41] Misiak, A. (1989), n-inner product spaces, Math. Nachr., 140, 299-319.
[42] Gunawan, H. and Mashadi, M. (2001), On n-normed spaces, Int. J. Math. Math. Sci., 27, 631-639.
[43] Savaş, E., Iθ summability methods in intuitionistic fuzzy n-normed spaces, (to appear)
[44] Debnath, P. and Sen, M. (2013), Some completeness results in terms of infinite series and quotient spaces in intuitionistic fuzzy nnormed linear spaces, Journal of Intelligent & Fuzzy Systems.
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