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On a new space \(m^2(M, A, \phi, p)\) of double sequences. (English) Zbl 1285.46001

Summary: We introduce a new space \(m^2(M, A, \phi, p)\) of double sequences related to \(p\)-absolute convergent double sequence space, combining an Orlicz function and an infinite double matrix. We study some properties of \(m^2(M, A, \phi, p)\) and obtain some inclusion relations involving \(m^2(M, A, \phi, p)\).

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)

Keywords:

sequence space
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[1] V. A. Khan, “On \Delta vm-Cesáro summable double sequences,” Thai Journal of Mathematics, vol. 10, no. 3, pp. 535-539, 2012. · Zbl 1275.40001
[2] V. A. Khan and S. Tabassum, “Statistically pre-Cauchy double sequences,” Southeast Asian Bulletin of Mathematics, vol. 36, no. 2, pp. 249-254, 2012. · Zbl 1265.40020
[3] V. A. Khan, S. Tabassum, and A. Esi, “Statistically convergent double sequence spaces in n-normed spaces,” ARPN Journal of Science and Technology, vol. 2, no. 10, pp. 991-995, 2012. · Zbl 1288.46022
[4] B. V. Limaye and M. Zeltser, “On the Pringsheim convergence of double series,” Proceedings of the Estonian Academy of Sciences, vol. 58, no. 2, pp. 108-121, 2009. · Zbl 1206.40004
[5] J. Lindenstrauss and L. Tzafriri, “On Orlicz sequence spaces,” Israel Journal of Mathematics, vol. 10, pp. 379-390, 1971. · Zbl 0227.46042
[6] V. A. Khan and S. Tabassum, “Statistically convergent double sequence spaces in 2-normed spaces defined by Orlicz function,” Applied Mathematics, vol. 2, no. 4, pp. 398-402, 2011.
[7] V. A. Khan and S. Tabassum, “On some new quasi almost \Delta m-lacunary strongly P-convergent double sequences defined by Orlicz functions,” Journal of Mathematics and Applications, vol. 34, pp. 45-52, 2011. · Zbl 1382.40015
[8] V. A. Khan and S. Tabassum, “On ideal convergent difference double sequence spaces in 2-normed spaces defined by Orlicz functions,” JMI International Journal of Mathematics and Applications, vol. 1, no. 2, pp. 26-34, 2010.
[9] V. A. Khan and S. Tabassum, “Some vector valued multiplier difference double sequence spaces in 2-normed spaces defined by Orlicz functions,” Journal of Mathematical and Computational Science, vol. 1, no. 1, pp. 126-139, 2011.
[10] V. A. Khan and S. Tabassum, “On some new double sequence spaces of invariant means defined by Orlicz functions,” Communications de la Faculté des Sciences de l’Université d’Ankara A1, vol. 60, no. 2, pp. 11-21, 2011. · Zbl 1281.46006
[11] V. A. Khan and S. Tabassum, “The strongly summable generalized difference double sequence spaces in 2-normed spaces defined by Orlicz functions,” Journal of Mathematical Notes, vol. 7, no. 2, pp. 45-58, 2011.
[12] V. A. Khan and S. Tabassum, “On some new almost double Lacunary \Delta m-squence spaces dened by Orlicz functions,” Journal of Mathematical Notes, vol. 6, no. 2, pp. 80-94, 2011.
[13] V. A. Khan, S. Tabassum, and A. Esi, “A\sigma double sequence spaces and statistical convergence in 2-normed spaces dened by Orlicz functions,” Theory and Applications of Mathematics and Computer Science, vol. 2, no. 1, pp. 61-71, 2012. · Zbl 1288.46022
[14] W. L. C. Sargent, “Some sequence spaces related to the lp spaces,” Journal of the London Mathematical Society, vol. 35, pp. 161-171, 1960. · Zbl 0090.03703
[15] Y. Altun and T. Bilgin, “On a new class of sequences related to the lp space defined by Orlicz function,” Taiwanese Journal of Mathematics, vol. 13, no. 4, pp. 1189-1196, 2009. · Zbl 1190.46006
[16] A. Esi, “On a class of new type difference sequence spaces related to the space lp,” Far East Journal of Mathematical Sciences, vol. 13, no. 2, pp. 167-172, 2004. · Zbl 1071.46008
[17] B. C. Tripathy and S. Mahanta, “On a class of sequences related to the lp space defined by Orlicz functions,” Soochow Journal of Mathematics, vol. 29, no. 4, pp. 379-391, 2003. · Zbl 1046.46007
[18] D. Rath, “Spaces of r-convex sequences and matrix transformations,” Indian Journal of Mathematics, vol. 41, no. 2, pp. 265-280, 1999. · Zbl 1037.40003
[19] D. Rath and B. C. Tripathy, “Characterization of certain matrix operators,” Orissa Mathematical Society, vol. 8, pp. 121-134, 1989.
[20] B. C. Tripathy and M. Sen, “On a new class of sequences related to the space lp,” Tamkang Journal of Mathematics, vol. 33, no. 2, pp. 167-171, 2002. · Zbl 1005.46002
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