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 |
. |
Category:
|
math |
. |
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 |
. |
Date available:
|
2014-09-01T08:16:00Z |
Last updated:
|
2020-01-05 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143920 |
. |
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 |
. |