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$A$-sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function. (English) Zbl 1230.46018
Summary: We study some new $A$-sequence spaces using ideal convergence and an Orlicz function in 2-normed space, and we give some relations related to these sequence spaces.
MSC:
46B45Banach sequence spaces
40A35Ideal and statistical convergence
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Full Text: DOI
References:
[1] P. Kostyrko, T. \vSalát, and W. Wilczyński, “I-convergence,” Real Analysis Exchange, vol. 26, no. 2, pp. 669-685, 2000.
[2] B. K. Lahiri and P. Das, “I and I\ast -convergence in topological spaces,” Mathematica Bohemica, vol. 130, no. 2, pp. 153-160, 2005. · Zbl 1111.40001 · http://mb.math.cas.cz/mb130-2/ · eudml:225306
[3] P. Kostyrko, M. Ma\vcaj, T. \vSalát, and M. Sleziak, “I-convergence and extremal I-limit points,” Mathematica Slovaca, vol. 55, no. 4, pp. 443-464, 2005. · Zbl 1113.40001 · eudml:32332
[4] P. Das, P. Kostyrko, W. Wilczyński, and P. Malik, “I and I\ast -convergence of double sequences,” Mathematica Slovaca, vol. 58, no. 5, pp. 605-620, 2008. · Zbl 1199.40026 · doi:10.2478/s12175-008-0096-x
[5] P. Das and P. Malik, “On the statistical and I- variation of double sequences,” Real Analysis Exchange, vol. 33, no. 2, pp. 351-363, 2008. · Zbl 1160.40003
[6] S. Gähler, “2-metrische Räume und ihre topologische Struktur,” Mathematische Nachrichten, vol. 26, pp. 115-148, 1963. · Zbl 0117.16003 · doi:10.1002/mana.19630260109
[7] H. Gunawan and Mashadi, “On finite-dimensional 2-normed spaces,” Soochow Journal of Mathematics, vol. 27, no. 3, pp. 321-329, 2001. · Zbl 1003.46007
[8] R. W. Freese and Y. J. Cho, Geometry of Linear 2-Normed Spaces, Nova Science Publishers, Hauppauge, NY, USA, 2001. · Zbl 1051.46001
[9] A. \cSahiner, M. Gürdal, S. Saltan, and H. Gunawan, “Ideal convergence in 2-normed spaces,” Taiwanese Journal of Mathematics, vol. 11, no. 5, pp. 1477-1484, 2007. · Zbl 1134.46302
[10] E. Sava\cs, “On some new sequence spaces in n-normed spaces using ideal convergence and an Orlicz function,” Journal of Inequalities and Applications, vol. 2010, Article ID 482392, 8 pages, 2010. · doi:10.1155/2011/592840
[11] B. C. Tripathy and B. Hazarika, “I-convergent sequence spaces associated with multiplier sequences,” Mathematical Inequalities & Applications, vol. 11, no. 3, pp. 543-548, 2008. · Zbl 1167.46005
[12] B. C. Tripathy and B. Hazarika, “Paranorm I-convergent sequence spaces,” Mathematica Slovaca, vol. 59, no. 4, pp. 485-494, 2009. · Zbl 1240.46015 · doi:10.2478/s12175-009-0141-4
[13] M. Gürdal, A. \cSahiner, and I. A\ccık, “Approximation theory in 2-Banach spaces,” Nonlinear Analysis, vol. 71, no. 5-6, pp. 1654-1661, 2009. · Zbl 1185.46004 · doi:10.1016/j.na.2009.01.030
[14] M. A. Krasnoselskii and Y. B. Rutisky, Convex Function and Orlicz Spaces, P. Noordhoff, Groningen, The Netherlands, 1961.
[15] S. D. Parashar and B. Choudhary, “Sequence spaces defined by Orlicz functions,” Indian Journal of Pure and Applied Mathematics, vol. 25, no. 4, pp. 419-428, 1994. · Zbl 0802.46020
[16] B. C. Tripathy, M. ET, and Y. Altin, “Generalized difference sequence spaces defined by Orlicz function in a locally convex space,” Journal of Analysis and Applications, vol. 1, no. 3, pp. 175-192, 2003. · Zbl 1058.46004
[17] A. Sahiner and M. Gurdal, “New sequence spaces in n-spaces with respect to an Orlicz function,” The Aligarh Bulletin of Mathematics, vol. 27, no. 1, pp. 53-58, 2008.
[18] W. H. Ruckle, “FK spaces in which the sequence of coordinate vectors is bounded,” Canadian Journal of Mathematics, vol. 25, pp. 973-978, 1973. · Zbl 0267.46008 · doi:10.4153/CJM-1973-102-9
[19] I. J. Maddox, “Sequence spaces defined by a modulus,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 100, no. 1, pp. 161-166, 1986. · Zbl 0631.46010 · doi:10.1017/S0305004100065968
[20] R. \cColak, M. Et, and E. Malkowsky, “Strongly almost (w, \lambda )-summable sequences defined by Orlicz functions,” Hokkaido Mathematical Journal, vol. 34, no. 2, pp. 265-276, 2005. · Zbl 1099.46004
[21] E. Sava\cs and R. F. Patterson, “An Orlicz extension of some new sequence spaces,” Rendiconti dell’Istituto di Matematica dell’Università di Trieste, vol. 37, no. 1-2, pp. 145-154, 2005. · Zbl 1119.46006
[22] B. C. Tripathy and P. Chandra, “On some generalized difference paranormed sequence spaces associated with multiplier sequence defined by modulus function,” Analysis in Theory and Applications, vol. 27, no. 1, pp. 21-27, 2011. · Zbl 1249.46005 · doi:10.1007/s10496-011-0021-y
[23] B. C. Tripathy and S. Mahanta, “On a class of generalized lacunary difference sequence spaces defined by Orlicz functions,” Acta Mathematicae Applicatae Sinica, vol. 20, no. 2, pp. 231-238, 2004. · Zbl 1071.46010 · doi:10.1007/s10255-004-0163-1
[24] E. Sava\cs, “\Delta m-strongly summable sequences spaces in 2-normed spaces defined by ideal convergence and an Orlicz function,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 271-276, 2010. · Zbl 1208.46004 · doi:10.1016/j.amc.2010.05.057
[25] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, London, UK, 1970. · Zbl 0193.08601