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Almost conservative four-dimensional matrices through de la Vallée-Poussin mean. (English) Zbl 07022344
Summary: The purpose of this paper is to generalize the concept of almost convergence for double sequence through the notion of de la Vallée-Poussin mean for double sequences. We also define and characterize the generalized regularly almost conservative and almost coercive four-dimensional matrices. Further, we characterize the infinite matrices which transform the sequence belonging to the space of absolutely convergent double series into the space of generalized almost convergence.

MSC:
40A05 Convergence and divergence of series and sequences
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[1] Banach, S., Théorie des Operations Lineaires, (1932) · JFM 58.0420.01
[2] Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Mathematica, 80, 167-190, (1948) · Zbl 0031.29501
[3] Mohiuddine, S. A., An application of almost convergence in approximation theorems, Applied Mathematics Letters, 24, 11, 1856-1860, (2011) · Zbl 1252.41022
[4] Móricz, F.; Rhoades, B. E., Almost convergence of double sequences and strong regularity of summability matrices, Mathematical Proceedings of the Cambridge Philosophical Society, 104, 2, 283-294, (1988) · Zbl 0675.40004
[5] Mursaleen, M.; Mohiuddine, S. A., Banach limit and some new spaces of double sequences, Turkish Journal of Mathematics, 36, 1, 121-130, (2012) · Zbl 1248.46006
[6] Başarir, M., On the strong almost convergence of double sequences, Periodica Mathematica Hungarica, 30, 3, 177-181, (1995) · Zbl 0819.40001
[7] Başar, F.; Kirişçi, M., Almost convergence and generalized difference matrix, Computers & Mathematics with Applications, 61, 3, 602-611, (2011) · Zbl 1217.40001
[8] Čunjalo, F., Almost convergence of double subsequences, Filomat, 22, 2, 87-93, (2008) · Zbl 1274.40021
[9] Kayaduman, K.; Çakan, C., The cesáro core of double sequences, Abstract and Applied Analysis, 2011, (2011) · Zbl 1235.40005
[10] Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, Journal of Mathematical Analysis and Applications, 293, 2, 523-531, (2004) · Zbl 1043.40002
[11] Mursaleen; Edely, O. H. H., Almost convergence and a core theorem for double sequences, Journal of Mathematical Analysis and Applications, 293, 2, 532-540, (2004) · Zbl 1043.40003
[12] Zeltser, M.; Mursaleen, M.; Mohiuddine, S. A., On almost conservative matrix methods for double sequence spaces, Publicationes Mathematicae Debrecen, 75, 3-4, 387-399, (2009) · Zbl 1212.40009
[13] Pringsheim, A., Zur theorie der zweifach unendlichen zahlenfolgen, Mathematische Annalen, 53, 3, 289-321, (1900) · JFM 31.0249.01
[14] Altay, B.; Başar, F., Some new spaces of double sequences, Journal of Mathematical Analysis and Applications, 309, 1, 70-90, (2005) · Zbl 1093.46004
[15] Hamilton, H. J., Transformations of multiple sequences, Duke Mathematical Journal, 2, 1, 29-60, (1936) · JFM 62.0214.01
[16] Mohiuddine, S. A.; Alotaibi, A., Some spaces of double sequences obtained through invariant mean and related concepts, Abstract and Applied Analysis, 2013, (2013) · Zbl 1277.46003
[17] Mursaleen; Mohiuddine, S. A., Double \(\sigma\)-multiplicative matrices, Journal of Mathematical Analysis and Applications, 327, 2, 991-996, (2007) · Zbl 1107.40004
[18] Mursaleen, M.; Mohiuddine, S. A., On \(\sigma\)-conservative and boundedly \(\sigma\)-conservative four-dimensional matrices, Computers & Mathematics with Applications, 59, 2, 880-885, (2010) · Zbl 1189.40005
[19] Schaefer, P., Infinite matrices and invariant means, Proceedings of the American Mathematical Society, 36, 104-110, (1972) · Zbl 0255.40003
[20] Robison, G. M., Divergent double sequences and series, Transactions of the American Mathematical Society, 28, 1, 50-73, (1926) · JFM 52.0223.01
[21] King, J. P., Almost summable sequences, Proceedings of the American Mathematical Society, 17, 1219-1225, (1966) · Zbl 0151.05701
[22] Schaefer, P., Matrix transformations of almost convergent sequences, Mathematische Zeitschrift, 112, 321-325, (1969) · Zbl 0181.33501
[23] Başar, F.; Solak, I., Almost-coercive matrix transformations, Rendiconti di Matematica e delle sue Applicazioni, 11, 2, 249-256, (1991) · Zbl 0732.40002
[24] Móricz, F., Extensions of the spaces \(c\) and \(c_0\) from single to double sequences, Acta Mathematica Hungarica, 57, 1-2, 129-136, (1991) · Zbl 0781.46025
[25] Mursaleen, M.; Mohiuddine, S. A., Regularly \(\sigma\)-conservative and \(\sigma\)-coercive four dimensional matrices, Computers & Mathematics with Applications, 56, 6, 1580-1586, (2008) · Zbl 1155.40303
[26] Eizen, C.; Laush, G., Infinite matrices and almost convergence, Mathematica Japonica, 14, 137-143, (1969) · Zbl 0195.06702
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