International Journal of Mathematics Trends and Technology
Volume 6 | Number 1 | Year 2014 | Article Id. IJMTT-V6P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V6P510
In this paper,we introduce and study a new class c0 (S, M, u–) of normed space S valued sequences using Orlicz function M as a generalization of basic space of null complex sequences c0. Beside the investigation pertaining to the containment relations of the class c0 (S, M, u–) for the various values of u– our primary interest is to explore its linear topological structures when topologized it with suitable natural paranorm.
[1] A. Wilansky, Modern methods in topological vector spaces , Mc Graw_Hill Book Co.Inc.New York , 1978.
[2] C.A. Bektas, and Y. Altin , Sequence space lM (p, q, s) on semi normed spaces, Indian J. Pure Appl. Math. 34 (4) , (2003),529–534.
[3] D. Ghosh, and P.D. Srivastava, On some vector valued sequence spaces using Orlicz function, Glasnik Matematicki, 34 (54), (1999), 253–261.
[4] E. Kolk, Topologies in generalized Orlicz sequence spaces, Filomat, 25(4), (2011), 191–211.
[5] E. Savas, and F. Patterson, An Orlicz extension of some new sequence spaces, Rend. Instit. Mat. Univ. Trieste , 37, (2005), 145–154.
[6] I.J. Maddox,. Some properties of paranormed sequence spaces, London, J. Math. Soc. 2(1), (1969), 316–322.
[7] J. Lindenstrauss, and L.Tzafriri, Classical Banach spaces, Springer-Verlag, New York , 1977.
[8] J.K. Srivastava, and N.P. Pahari, On Banach space valued sequence space c0 (X, M, l–, p–, L) defined by Orlicz function, Jour. of Rajasthan Academy of Physical Sciences, 11(2) , (2011), 103-116.
[9] J.K. Srivastava, and N.P. Pahari, On 2-Banach space valued paranormed sequence space c0 (X, M, ||.,.||, l–, p–) defined by Orlicz function, Jour. of Rajasthan Academy of Physical Sciences, 12(3) , (2013), 319-338.
[10] M. Basariv, and S. Altundag, On generalized paranormed statistically convergent sequence spaces defined by Orlicz function, Handawi. Pub. Cor., J. of Inequality and Applications, 2009 (2009), 1-13.
[11] M.A. Krasnosel'skiî, and Y.B. Rutickiî, Convex functions and Orlicz spaces, P. Noordhoff Ltd-Groningen-The Netherlands, 1961.
[12] N.P. Pahari, On certain topological structures of paranormed Orlicz space (S ((X ,||.||),, –,u– ), F ) of vector valued sequences, International Jour. of Mathematical Archive , 4 (11), (2011), 231-241.
[13] N.P. Pahari , On certain topological structures of normed space valued generalized Orlicz function space. International Jour. of Scientific Engineering and Research (IJSER), 2(1), ( 2014), 61–66.
[14] P.K. Kamthan, and M. Gupta, Sequence spaces and series , Lecture notes in pure and applied mathematics, Marcel Dekker, New York, 1981.
[15] Rao, K. C. & Subremanina, N.. The Orlicz space of entire sequences, IJMass, 68, (2004), 3755– 3764.
[16] S.D. Parashar, and B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25(4), (1994), 419–428.
[17] V.A. Khan, On a new sequence space defined by Orlicz functions, Common. Fac. Sci. Univ. Ank-series, 57( 2), (2008), 25–33.
[18] V.N. Bhardwaj, and I. Bala, Banach space valued sequence space M (X, p), Int. J. of Pure and Appl. Maths., 41(5), (2007), 617–626.
[19] V. Karakaya, Some new sequence spaces defined by a sequence of Orlicz functions, Taiwanese J. of Maths. 9(4),(2005),617–627.
[20] W.H. Ruckle, Sequence spaces , Pitman Advanced Publishing Programme, 1981.
Narayan Prasad Pahari, "On Normed Space Valued Total Paranormed Orlicz Space of Null Sequences and its Topological Structures," International Journal of Mathematics Trends and Technology (IJMTT), vol. 6, no. 1, pp. 105-112, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V6P510
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