On
DOI:
https://doi.org/10.33993/jnaat432-1028Keywords:
statistical convergence,Abstract
Recently in [19], Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion ofDownloads
References
C. Alsina, B. Schweizer and A. Sklar, Continuity properties of probabilistic norms, J. Math. Anal. Appl., 208 (1997), pp. 446-452, http://dx.doi.org/10.1006/jmaa.1997.5333 DOI: https://doi.org/10.1006/jmaa.1997.5333
H. Çakalli, A study on statistical convergence, Funct. Anal. Approx. Comput., 1(2) (2009), pp. 19-24, MR2662887.
J.Connor and M.A. Swardson, Measures and ideals of C∗(X), Ann. N. Y. Acad. Sci., 704 (1993), pp. 80--91. DOI: https://doi.org/10.1111/j.1749-6632.1993.tb52511.x
A. Esi and M. K. Özdemir, Generalized Δm-Statistical convergence in probabilistic normed space, J. Comput. Anal. Appl., 13(5) (2011), pp. 923-932.
H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), pp. 241-244. DOI: https://doi.org/10.4064/cm-2-3-4-241-244
J. A. Fridy, On statistical convergence, Analysis, 5 (1985) pp. 301--313. DOI: https://doi.org/10.1524/anly.1985.5.4.301
S. Gähler, 2-metrische Raume and ihre topologische Struktur, Math. Nachr., 26 (1963), pp. 115-148, http://dx.doi.org/10.1002/mana.19630260109 DOI: https://doi.org/10.1002/mana.19630260109
I . Goleţ, On probabilistic 2-normed spaces, Novi Sad J. Math., 35 (2006), pp. 95-102.
M. Gürdal and S. Pehlivan, Statistical convergence in 2-normed spaces, South. Asian Bull. Math., 33 (2009), pp. 257-264.
M. Gürdal and S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math., 2(1) (2004), pp. 107-113.
S. Karakus, Statistical convergence on probabilistic normed spaces, Math. Commun., 12 (2007), pp. 11-23. DOI: https://doi.org/10.1155/2007/14737
S. Karakus, K. Demirci and O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons and Fractals, 35 (2008), pp. 763-769, http://dx.doi.org/10.1016/j.chaos.2006.05.046 DOI: https://doi.org/10.1016/j.chaos.2006.05.046
V. Kumar and M. Mursaleen, On (λ,μ)-statistical convergence of double sequences on intuitionistic fuzzy normed spaces, Filomat, 25(2) (2011), pp. 109-120. DOI: https://doi.org/10.2298/FIL1102109K
L. Leindler, Uber die de la Vallee-Pousinsche Summierbarkeit allgenmeiner Othogonalreihen, Acta Math. Acad. Sci. Hungar, 16 (1965), pp. 375-387. DOI: https://doi.org/10.1007/BF01904844
I. J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Cambridge Philos. Soc., 104(1) (1988), pp. 141-145, http://dx.doi.org/10.1017/S0305004100065312 DOI: https://doi.org/10.1017/S0305004100065312
G. D. Maio and L. D. R. Kočinac, Statistical convergence in topology, Topology Appl., 156 (2008), pp. 28-45, http://dx.doi.org/10.1016/j.topol.2008.01.015 DOI: https://doi.org/10.1016/j.topol.2008.01.015
K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA, 28 (1942), pp. 535-537. DOI: https://doi.org/10.1073/pnas.28.12.535
H. I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(5) (1995), pp. 1811-1819. DOI: https://doi.org/10.1090/S0002-9947-1995-1260176-6
M. Mursaleen, Statistical convergence in random 2-normed spaces, Acta Sci. Math. (Szeged), 76(1-2) (2010), pp. 101-109. DOI: https://doi.org/10.1007/BF03549823
M. Mursaleen, λ-statistical convergence, Mathematica Slovaca, 50(1) (2000), pp. 111-115.
M. Mursaleen and A. K. Noman, On the spaces of λ-convergent and bounded sequences, Thai J. Math., 8(2) (2010), pp. 311-329.
M. Mursaleen and A. Alotaibi, Statistical summability and approximation by de la Vallee-Pousin mean, Applied Math. Letters, 24 (2011), pp. 320—324, http://dx.doi.org/10.1016/j.aml.2010.10.014 DOI: https://doi.org/10.1016/j.aml.2010.10.014
M. Mursaleen, C. Çakan, S. A. Mohiuddine and E. Savaş, Generalized statistical convergence and statistical core of double sequences, Acta Math. Sinica, 26(11) (2010), pp. 2131-2144, http://dx.doi.org/10.1007/s10114-010-9050-2 DOI: https://doi.org/10.1007/s10114-010-9050-2
M. Mursaleen and Osama H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), pp. 223-231, http://dx.doi.org/10.1016/j.jmaa.2003.08.004 DOI: https://doi.org/10.1016/j.jmaa.2003.08.004
M. Mursaleen and Osama H. H. Edely, Generalized statistical convergence, Information Sciences, 162 (2004), pp. 287-294. DOI: https://doi.org/10.1016/j.ins.2003.09.011
M. Mursaleen and Osama H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Letters, 22 (2009), pp. 1700-1704, http://dx.doi.org/10.1016/j.aml.2009.06.005 DOI: https://doi.org/10.1016/j.aml.2009.06.005
S. A. Mohiuddine and Q.M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos, Solitons and Fractals, 42 (2009), pp. 1731-1737, http://dx.doi.org/10.1016/j.chaos.2009.03.086 DOI: https://doi.org/10.1016/j.chaos.2009.03.086
M. Mursaleen and S.A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233(2) (2009), pp. 142-149, http://dx.doi.org/10.1016/j.cam.2009.07.005 DOI: https://doi.org/10.1016/j.cam.2009.07.005
T. Salát, On statistical convergence sequences of real numbers, Math. Slovaca, 30 (1980), pp. 139-150.
I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), pp. 361-375. DOI: https://doi.org/10.2307/2308747
B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), pp. 313-334. DOI: https://doi.org/10.2140/pjm.1960.10.313
B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland, New York- Amsterdam-Oxford, 1983.
C. Sempi, A short and partial history of probabilistic normed spaces, Mediterr. J. Math., 3 (2006), pp. 283-300, http://dx.doi.org/10.1007/s00009-006-0078-6 DOI: https://doi.org/10.1007/s00009-006-0078-6
C. Şençimen and S. Pehlivan, Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159 (2008), pp. 361-370, http://dx.doi.org/10.1016/j.fss.2007.06.008 DOI: https://doi.org/10.1016/j.fss.2007.06.008
A. N. Serstnev, On the notion of a random normed space, Dokl. Akad. Nauk SSSR 149 (1963), pp. 280-283.
On generalized statistical convergence in random 2-normed space, Iranian Journal of Science & Technology, (2012) A4: 417-423. DOI: https://doi.org/10.1186/1029-242X-2012-209
Published
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
