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Kılıçman, Adem; Borgohain, Stuti

Some new classes of generalized difference strongly summable \(n\)-normed sequence spaces defined by ideal convergence and Orlicz function. (English) Zbl 1474.46034

Abstr. Appl. Anal. 2014, Article ID 621383, 7 p. (2014).
Summary: We study some new generalized difference strongly summable \(n\)-normed sequence spaces using ideal convergence and an Orlicz function in connection with de la Vallèe Poussin mean. We give some relations related to these sequence spaces also.

Cited in 2 Documents

MSC:

46B20 Geometry and structure of normed linear spaces
40C05 Matrix methods for summability
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\textit{A. Kılıçman} and \textit{S. Borgohain}, Abstr. Appl. Anal. 2014, Article ID 621383, 7 p. (2014; Zbl 1474.46034)
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References:

[1] Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Mathematica, 80, 167-190 (1948) · Zbl 0031.29501
[2] Maddox, I. J., Spaces of strongly summable sequences, The Quarterly Journal of Mathematics, 18, 345-355 (1967) · Zbl 0156.06602
[3] Schaefer, P., Infinite matrices and invariant means, Proceedings of the American Mathematical Society, 36, 104-110 (1972) · Zbl 0255.40003
[4] Mursaleen, M., Matrix transformations between some new sequence spaces, Houston Journal of Mathematics, 9, 4, 505-509 (1983) · Zbl 0542.40003
[5] Kostyrko, P.; Salat, T.; Wilczynski, W., On \(I\)-convergence, Real Analysis Exchange, 26, 2, 669-685 (2001) · Zbl 1021.40001
[6] Lindenstrauss, J.; Tzafriri, L., On Orlicz sequence spaces, Israel Journal of Mathematics, 10, 379-390 (1971) · Zbl 0227.46042
[7] Kızmaz, H., On certain sequence spaces, Canadian Mathematical Bulletin, 24, 2, 169-176 (1981) · Zbl 0454.46010
[8] Gähler, S., Lineare 2-normierte Räume, Mathematische Nachrichten, 28, 1-43 (1964) · Zbl 0142.39803
[9] Misiak, A., \(n\)-inner product spaces, Mathematische Nachrichten, 140, 299-319 (1989) · Zbl 0673.46012
[10] Gurdal, M., On ideal convergent sequences in 2-normed spaces, Thai Journal of Mathematics, 4, 1, 85-91 (2006) · Zbl 1155.40300
[11] Gurdal, M.; Sahiner, A., Ideal convergence in \(n\)-normed spaces and some new sequence spaces via \(n\)-norm, Journal of Fundamental Sciences, 4, 1, 233-244 (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.