Some vector valued multiplier difference sequence spaces defined by a sequence of Orlicz functions
Автор: Dutta Hemen
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.13, 2011 года.
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In this article we introduce some new difference sequence spaces with a real 2-normed linear space as base space and which are defined using a sequence of Orlicz functions, a bounded sequence of positive real numbers and a sequence of non-zero reals as multiplier sequence. We show that these spaces are complete paranormed spaces when the base space is a 2-Banach space and investigate these spaces for solidity, symmetricity, convergence free, monotonicity and sequence algebra. Further we obtain some relation between these spaces as well as prove some inclusion results.
Difference sequence, 2-norm, orlicz function, paranorm, completeness, solidity, symmetricity, convergence free, monotone space.
Короткий адрес: https://sciup.org/14318344
IDR: 14318344
Список литературы Some vector valued multiplier difference sequence spaces defined by a sequence of Orlicz functions
- Dutta H. Some results on 2-normed spaces//Novi Sad J. Math.-(To appear).
- Dutta H. Characterization of certain matrix classes involving generalized difference summability spaces//Appl. Sci. (APPS).-Vol. 11.-2009.-P. 60-67.
- Dutta H. On some complete metric spaces of strongly summable sequences of fuzzy numbers//Rend. Semin. Math.-2010.-Vol. 68, № 1.-P. 29-36.
- Et M., Colak R. On generalized difference sequence spaces//Soochow J. Math.-1995.-Vol. 21.-P. 377-386.
- Gähler S. 2-metrische Räume ind ihre topologische struktur//Math. Nachr.-1963.-Vol. 28.-P. 115-148.
- Gähler S. Linear 2-normietre Räume//Math. Nachr.-1965.-Vol. 28.-P. 1-43.
- Gähler S. Uber der uniformisierbarkeit 2-metrische Räume//Math. Nachr.-1965.-Vol. 28.-P. 235-244.
- Goes G., Goes S. Sequences of bounded variation and sequences of Fourier coefficients//Math. Zeift.-1970.-Vol. 118.-P. 93-102.
- Ghosh D., Srivastava P. D. On some vector valued sequence spaces defined using a modulus function//Indian J. Pure Appl. Math.-1999.-Vol. 30, № 8.-P. 819-826.
- Gunawan H., Mashadi M. On finite dimensional 2-normed spaces//Soochow J. Math.-2001.-Vol. 27, № 3.-P. 321-329.
- Kizmaz H. On certain sequence spaces//Canad. Math. Bull.-1981.-Vol. 24, № 2.-P. 169-176..
- Lascarides C. G. A study of certain sequece spaces of maddox and generalization of a theorem of Iyer//Pacific J. Math.-1971.-Vol. 38, № 2.-P. 487-500.
- Lascarides C. G., Maddox I. J. Matrix transformation between some classes of sequences//Prov. Camb. Phil. Soc.-1970.-Vol. 68.-P. 99-104.
- Lindenstrauss J., Tzafriri L. On Orlicz sequence spaces//Israel J. Math.-1971.-Vol. 10.-P. 379-390.
- Maddox I. J. Paranormed sequence spaces generated by infinite matrices//Proc. Camb. Phil. Sco.-1968.-Vol. 64.-P. 335-340.
- Mursaleen, Khan M. A., Quamaruddin. Difference sequence spaces defined by Orlicz functions//Demonstratio Math.-1999.-Vol. 32, № 1.-P. 145-150.
- Nakano H. Modular sequence space//Proc. Japan Acad.-1951.-Vol. 27.-P. 508-512.
- Nanda S. Some sequence spaces and almost convergence//J. Austral. Math. Soc. Ser. A.-1976.-Vol. 22.-P. 446-455.
- Parasar S. D., Choudhary B. Sequence spaces defined by Orlicz functions//Indian J. Pure Appl. Math.-1994.-Vol. 25, № 4.-P. 419-428.
- Simons S. The sequence spaces $\ell(p_v)$ and $m(p_v)$//Proc. London. Math. Soc.-1965.-Vol. 15.-P. 422-436.
- Tripathy B. C. A class of difference sequences related to the p-normed space $\ell^p$//Demonstratio Math.-2003.-Vol. 36, № 4.-P. 867-872.
