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Title: Double Sequence Spaces Definedby a Sequence of Modulus Functions over $n$-normed Spaces (English)
Author: Sharma, Sunil K.
Author: Esi, Ayhan
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 53
Issue: 1
Year: 2014
Pages: 117-134
Summary lang: English
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Category: math
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Summary: In the present paper we introduce some double sequence spaces defined by a sequence of modulus function $ F = (f_{k,l})$ over $n$-normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces. (English)
Keyword: double sequences
Keyword: $P$-convergent
Keyword: modulus function
Keyword: paranorm space
MSC: 40C05
MSC: 42B15
idZBL: Zbl 06416946
idMR: MR3331075
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Date available: 2014-09-01T08:16:00Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/143920
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Reference: [1] Altay, B., Başar, F.: Some new spaces of double sequencs. J. Math. Anal. Appl. 309 (2005), 70–90. MR 2154028, 10.1016/j.jmaa.2004.12.020
Reference: [2] Altin, Y.: Properties of some sets of sequences defined by a modulus function. Acta Math. Sci. Ser. B Engl. Ed. 29 (2009), 427–434. Zbl 1199.46019, MR 2517605, 10.1016/S0252-9602(09)60042-4
Reference: [3] Altin, Y., Et, M.: Generalized difference sequence spaces defined by a modulus function in a locally convex space. Soochow J. Math. 31 (2005), 233–243. Zbl 1085.46501, MR 2149876
Reference: [4] Altin, Y., Işik, M., Çolak, R.: A new sequence space defined by a modulus. Stud. Univ. Babes–Bolyai Math. 53 (2008), 3–13. Zbl 1212.46010, MR 2440755
Reference: [5] Altinok, H., Altin, Y., Işik, M.: The sequence space $Bv_\sigma (M,P,Q,S)$ on seminormed spaces. Indian J. Pure Appl. Math. 39 (2008), 49–58. Zbl 1153.46300, MR 2413756
Reference: [6] Başarir, M., Sonalcan, O.: On some double sequence spaces. J. Indian Acad. Math. 21 (1999), 193–200. Zbl 0978.40002, MR 1754919
Reference: [7] Başar, F., Sever, Y.: The space $\mathcal {L}_p$ of double sequences. Math. J. Okayama Univ. 51 (2009), 149–157. MR 2482412
Reference: [8] Bromwich, T. J.: An Introduction to the Theory of Infinite Series. Macmillan and co., Ltd., New York, 1965.
Reference: [9] Connor, J.: On strong matrix summability with respect to a modulus and statistical convergence. Canad. Math. Bull. 30 (1989), 194–198. Zbl 0693.40007, MR 1006746
Reference: [10] Esi, A.: Some new sequence spaces defined by a sequence of moduli. Turk. J. Math. 21 (1997), 61–68. Zbl 0914.46005, MR 1473301
Reference: [11] Esi, A.: Strongly $[V_2, \lambda _2, M, p]$-summable double sequence spaces defined by Orlicz function. Int. J. Nonlinear Anal. Appl. 2 (2011), 110–115. Zbl 1281.40003
Reference: [12] Et, M., Çolak, R.: On generalized difference sequence spaces. Soochow J. Math. 21, 4 (1995), 377–386.
Reference: [13] Gähler, S.: Linear 2-normietre RumeStatistical convergence in 2-normed spaces. Math. Nachr. 28 (1965), 1–43. Statistical convergence in 2-normed spaces Southeast Asian Bull. Math. 33, 2 (2009), 257–264.
Reference: [14] Gunawan, H.: On $n$-inner product, $n$-norms, and the Cauchy-Schwartz inequality. Sci. Math. Jap. 5 (2001), 47–54. MR 1885776
Reference: [15] Gunawan, H.: The space of $p$-summable sequence and its natural $n$-norm. Bull. Aust. Math. Soc. 64 (2001), 137–147. MR 1848086, 10.1017/S0004972700019754
Reference: [16] Gunawan, H., Mashadi, M.: On n-normed spaces. Int. J. Math. Math. Sci. 27 (2001), 631–639. Zbl 1006.46006, MR 1873126, 10.1155/S0161171201010675
Reference: [17] Hamilton, H. J.: Transformations of multiple sequences. Duke Math. J. 2 (1936), 29–60. Zbl 0013.30301, MR 1545904, 10.1215/S0012-7094-36-00204-1
Reference: [18] Hardy, G. H.: On the convergence of certain multiple series. Proc. Camb. Phil., Soc. 19 (1917), 86–95.
Reference: [19] Hardy, G. H.: Divergent Series. Oxford at the Clarendon Press, 1949. Zbl 0032.05801, MR 0030620
Reference: [20] Kizmaz, H.: On certain sequences spaces. Canad. Math. Bull. 24, 2 (1981), 169–176. MR 0619442, 10.4153/CMB-1981-027-5
Reference: [21] Maddox, I. J.: Sequence spaces defined by a modulus. Math. Proc. Cambridge Philos. Soc. 100 (1986), 161–166. Zbl 0631.46010, MR 0838663, 10.1017/S0305004100065968
Reference: [22] Malkowsky, E., Savaş, E.: Some $ \lambda $-sequence spaces defined by a modulus. Archivum Math. 36 (2000), 219–228. Zbl 1046.40011, MR 1785040
Reference: [23] Misiak, A.: $n$-inner product spaces. Math. Nachr. 140 (1989), 299–319. Zbl 0708.46025, MR 1015402, 10.1002/mana.19891400121
Reference: [24] Moricz, F.: Extension of the spaces $c $ and $c_0$ from single to double sequences. Acta Math. Hungarica 57 (1991), 129–136. MR 1128849, 10.1007/BF01903811
Reference: [25] Moricz, F., Rhoades, B. E.: Almost convergence of double sequences and strong reqularity of summability matrices. Math. Proc. Camb. Phil. Soc. 104 (1988), 283–294. MR 0948914, 10.1017/S0305004100065464
Reference: [26] Mursaleen, M.: Almost strongly regular matrices and a core theorem for double sequences. J. Math. Anal. Appl. 293, 2 (2004), 523–531. Zbl 1043.40002, MR 2053895, 10.1016/j.jmaa.2004.01.014
Reference: [27] Mursaleen, M., Edely, O. H. H.: Statistical convergence of double sequences. J. Math. Anal. Appl. 288, 1 (2003), 223–231. Zbl 1032.40001, MR 2019757, 10.1016/j.jmaa.2003.08.004
Reference: [28] Mursaleen, M., Edely, O. H. H.: Almost convergence and a core theorem for double sequences. J. Math. Anal. Appl. 293, 2 (2004), 532–540. Zbl 1043.40003, MR 2053896, 10.1016/j.jmaa.2004.01.015
Reference: [29] Pringsheim, A.: Zur Theori der zweifach unendlichen Zahlenfolgen. Math. Ann. 53 (1900), 289–321. MR 1511092, 10.1007/BF01448977
Reference: [30] Raj, K., Sharma, S. K.: Difference sequence spaces defined by sequence of modulus function. Proyecciones J. Math. 30 (2011), 189–199. MR 2852349
Reference: [31] Raj, K., Sharma, S. K.: Some difference sequence spaces defined by sequence of modulus function. Int. J. Math. Archive 2 (2011), 236–240.
Reference: [32] Robinson, G. M.: Divergent double sequences and series. Trans. Amer. Math. Soc. 28 (1926), 50–73. MR 1501332, 10.1090/S0002-9947-1926-1501332-5
Reference: [33] Savaş, E.: On some generalized sequence spaces defined by a modulus. Indian J. Pure Appl. Math. 30 (1999), 459–464. Zbl 0928.40006, MR 1694693
Reference: [34] Savaş, E., Patterson, R. F.: Double sequence spaces defined by a modulus. Math. Slovaca 61 (2011), 245–256. Zbl 1265.40029, MR 2786698, 10.2478/s12175-011-0009-2
Reference: [35] Tripathy, B. C.: Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex spaces. Soochow J. Math. 30 (2004), 431–446. MR 2106062
Reference: [36] Tripathy, B. C.: Statistically convergent double sequences. Tamkang J. Math. 34 (2003), 231–237. Zbl 1040.40001, MR 2001918
Reference: [37] Wilansky, A.: Summability through Functional Analysis. 85 North–Holland Math. Stud. 1984. Zbl 0531.40008, MR 0738632
Reference: [38] Zeltser, M.: Investigation of Double Sequence Spaces by Soft and Hard Analytical Methods. Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001. Zbl 1087.46004, MR 1833364
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