Previous |  Up |  Next

Article

Title: Double sequence spaces over $n$-normed spaces (English)
Author: Raj, Kuldip
Author: Sharma, Sunil K.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 50
Issue: 2
Year: 2014
Pages: 65-76
Summary lang: English
.
Category: math
.
Summary: In this paper, we define some classes of double sequences over $n$-normed spaces by means of an Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined. (English)
Keyword: paranorm space
Keyword: Orlicz function
Keyword: solid
Keyword: monotone
Keyword: double sequences
Keyword: $n$-normed space
MSC: 40A05
MSC: 40C05
MSC: 40D05
MSC: 46A70
idZBL: Zbl 06391566
idMR: MR3215280
DOI: 10.5817/AM2014-2-65
.
Date available: 2014-05-23T09:30:15Z
Last updated: 2015-03-19
Stable URL: http://hdl.handle.net/10338.dmlcz/143779
.
Reference: [1] Başarir, M., Sonalcan, O.: On some double sequence spaces.J. Indian Acad. Math. 21 (1999), 193–220. Zbl 0978.40002, MR 1754919
Reference: [2] Bromwich, T.J.: An Introduction to the Theory of Infinite Series.Macmillan and Co. Ltd., New York, 1965.
Reference: [3] Dutta, H.: An application of lacunary summability method to $n$-norm.Int. J. Appl. Math. Stat. 15 (09) (2009), 89–97. MR 2578559
Reference: [4] Dutta, H.: Characterization of certain matrix classes involving generalized difference summability spaces.Appl. Sci. 11 (2009), 60–67. Zbl 1195.40002, MR 2534057
Reference: [5] Dutta, H.: On n-normed linear space valued strongly (C,1)-summable difference sequences.Asian-Eur. J. Math. 3 (4) (2010), 565–575. Zbl 1213.46006, MR 2747386, 10.1142/S1793557110000441
Reference: [6] Dutta, H.: On sequence spaces with elements in a sequence of real linear n-normed spaces.Appl. Math. Lett. 23 (9) (2010), 1109–1113. Zbl 1207.46008, MR 2659147, 10.1016/j.aml.2010.04.045
Reference: [7] Dutta, H.: On some $n$-normed linear space valued difference sequences.J. Franklin Inst. B 348 (2011), 2876–2883. Zbl 1263.46023, MR 2847578, 10.1016/j.jfranklin.2011.09.010
Reference: [8] Dutta, H.: An Orlicz extension of difference sequences on real linear n-normed spaces.J. Inequal. Appl. 2013:232 (2013), 13pp. Zbl 1292.46002, MR 3066041, 10.1186/1029-242X-2013-232
Reference: [9] Dutta, H., Başar, F.: A generalization of Orlicz sequence spaces by Cesàro mean of order one.Acta Math. Univ. Comenian. (N.S.) 80 (2) (2011), 185–200. Zbl 1265.46004, MR 2835274
Reference: [10] Dutta, H., Bilgin, T.: Strongly $(V^\lambda , A, \Delta _{vm}^n, p)$-summable sequence spaces defined by an Orlicz function.Appl. Math. Lett. 24 (7) (2011), 1057–1062. MR 2784157, 10.1016/j.aml.2011.01.022
Reference: [11] Dutta, H., Reddy, B.S.: On non-standard $n$-norm on some sequence spaces.Int. J. Pure Appl. Math. 68 (1) (2011), 1–11. Zbl 1232.46005, MR 2798332
Reference: [12] Dutta, H., Reddy, B.S., Cheng, S.S.: Strongly summable sequences defined over real $n$-normed spaces.Appl. Math. E-Notes 10 (2010), 199–209. Zbl 1226.46018, MR 2732898
Reference: [13] Et, M., Çolak, R.: On generalized difference sequence spaces.Soochow J. Math. 21 (4) (1995), 377–386.
Reference: [14] Gähler, S.: Linear 2-normietre Rume.Math. Nachr. 28 (1965), 1–43. 10.1002/mana.19640280102
Reference: [15] Gunawan, H.: On $n$-inner product, $n$-norms, and the Cauchy-Schwartz inequality.Sci. Math. Jap. 5 (2001), 47–54. MR 1885776
Reference: [16] Gunawan, H.: The space of $p$-summable sequence and its natural $n$-norm.Bull. Austral. Math. Soc. 64 (2001), 137–147. MR 1848086, 10.1017/S0004972700019754
Reference: [17] 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: [18] Hardy, G.H.: On the convergence of certain multiple series.Proc. Camb. Phil., Soc. 19 (1917), 86–95.
Reference: [19] Karakaya, V., Dutta, H.: On some vector valued generalized difference modular sequence spaces.Filomat 25 (3) (2011), 15–27. Zbl 1265.46009, MR 2934370, 10.2298/FIL1103015K
Reference: [20] Kızmaz, H.: On certain sequences spaces.Canad. Math. Bull. 24 (2) (1981), 169–176. MR 0619442, 10.4153/CMB-1981-027-5
Reference: [21] Lindenstrauss, J., Tzafriri, L.: On Orlicz sequence spaces,.Israel J. Math. 10 (1971), 379–390. Zbl 0227.46042, MR 0313780, 10.1007/BF02771656
Reference: [22] Misiak, A.: $n$-inner product spaces.Math. Nachr. 140 (1989), 299–319. Zbl 0708.46025, MR 1015402, 10.1002/mana.19891400121
Reference: [23] Moricz, F.: Extension of the spaces $c $ and $c_0$ from single to double sequences.Acta Math. Hungar. 57 (1991), 129–136. MR 1128849, 10.1007/BF01903811
Reference: [24] 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: [25] Nakano, H.: Modular sequence spaces.Proc. Japan Acad. Ser. A Math. Sci. 27 (1951), 508–512. MR 0047929
Reference: [26] Raj, K., Sharma, A.K., Sharma, S.K.: A sequence space defined by Musielak-Orlicz functions.Int. J. Pure Appl. Math. 67 (2011), 472–484. MR 2814723
Reference: [27] Raj, K., Sharma, S.K., Sharma, A.K.: Some difference sequence spaces in $n$-normed spaces defined by Musielak-Orlicz function.Armen. J. math. 3 (2010), 127–141. MR 2792497
Reference: [28] Raj, K., Sharma, S.K., Sharma, A.K.: Some new sequence spaces defined by a sequence of modulus functions in $n$-normed spaces.Int. J. Math. Sci. Engg. Appl. 5 (2011), 395–403. MR 2797897
Reference: [29] Savaş, E.: On some new sequence spaces in 2-normed spaces using ideal convergence and an Orlicz function.J. Inequal. Appl. (2010), 8 pages, Article ID 482392. Zbl 1213.46009, MR 2721579
Reference: [30] Simons, S.: The sequence spaces $l(p_v)$ and $m(p_v)$.Proc. Japan Acad. 27 (1951), 508–512.
Reference: [31] Tripathy, B.C.: Statistically convergent double sequences.Tamkang J. Math. 34 (2003), 231–237. Zbl 1040.40001, MR 2001918
Reference: [32] 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: [33] Tripathy, B.C., Altin, Y., Et, M.: Generalized difference sequence spaces on seminormed space defined by Orlicz function.Math. Slovaca 58 (2008), 315–324. MR 2399244, 10.2478/s12175-008-0077-0
Reference: [34] Tripathy, B.C., Dutta, H.: On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary $\Delta _m^ n$ statistical convergence.An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. 20 (1) (2012), 417–430. MR 2928432
Reference: [35] Tripathy, B.C., Esi, A., Tripathy, B.K.: On a new type of generalized difference Cesàro sequence spaces.Soochow J. Math. 31 (3) (2005), 333–340. Zbl 1093.46507, MR 2167543
Reference: [36] Wilansky, A.: Summability through functional analysis.North-Holland Mathematics Studies, vol. 85, Amsterdam - New York - Oxford: North-Holland, 1984. Zbl 0531.40008, MR 0738632
.

Files

Files Size Format View
ArchMathRetro_050-2014-2_1.pdf 489.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo