Some new triple sequence spaces over n-normed space

  • Tanweer Jalal National Institute of Technology.
  • Ishfaq Ahmad National Institute of Technology.

Resumen

Triple sequence spaces were introduced by Sahiner et al. The main objective of this paper is to define some new classes of triple sequences over n-normed space by means of Museiak-Orlicz function and difference operators. We also study some algebraic and topological properties of these new sequence spaces.

Biografía del autor

Tanweer Jalal, National Institute of Technology.
Departamento de Matemáticas.
Ishfaq Ahmad, National Institute of Technology.
Departamento de Matemáticas.

Citas

[1] A. Alotaibi, M. Mursaleen and S. K. Sharma, Double sequence spaces over n-normed spaces defined by a sequence of orlicz functions, Jou. Ineq. Appl., 216, 2014:216, (2014).
[2] A. J. Datta, A. Esi and B.C. Tripathy, Statistically convergent triple sequence space defined by orlicz function, Jou. Math. Anal., 4, pp. 16-22, (2013).
[3] S. Debnath, B.C. Sarma Das, Some generalized triple sequence spaces of real numbers, Jou. Nonl. Anal. and Opt., 6, pp. 71-79, (2015).
[4] H. Dutta, An application of lacunary summability method to n-norm, Int. Jou. Appl. Math. Sat., 15 (D09), pp. 89-97, (2009).
[5] H. Dutta, On sequence spaces with elements in a sequence of real linear n-normed spaces, Appl. Math. Lett., 33(9), pp. 1109-113, (2010).
[6] H. Dutta, On some n-normed linear space valued difference sequence, Jou. Franklin Inst., 348, pp. 2876-2883, (2011).
[7] A. Esi, On some triple almost lacunary sequence spaces defined by orlicz functions, Research and Reviews: Discrete Mathematical structures 1, pp. 16-25, (2014).
[8] A. Esi, M.N. Catalbas, Almost convergence of triple sequences, G. Jou. Math. Anal., 2, pp. 6-10, (2014).
[9] A. Esi, E. Savas, On lacunary statically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9, pp. 2529-2534, (2015).
[10] M. Et, R. Colak, On generalized difference sequence spaces, Soochow Jou. Math., 21, 4, pp. 377-386, (1995).
[11] S. Gähler, Linear 2-normietre rume, Math. Nachr., 28, pp. 1-43, (1965).
[12] H. Gunawan, On n−inner product, n−norms, and the cauchySchwartz Inequality, Sci. Math. Jap., 5, pp. 47-54, (2001).
[13] H. Gunawan, The space of p−summable sequence and its natural n−norm, Bull. Austral. Math. Soc., 64, pp. 137-147, (2001).
[14] H. Gunawan, M. Mashadi, On n−normed spaces, Int. Jou. Math. Sci., 27, pp. 631-639, (2001).
[15] T. Jalal, Some new I-convergent sequence spaces defined by using a sequence of modulus functions in n−normed spaces, Int. Jou. Math. Archive, 5 (9), pp. 202-209, (2014).
[16] T. Jalal, On generalized A-difference sequence spaces defined by ideal convergence on a real n−normed space through lacunary sequences, Bull. Cal. Math. Soc., 106 (6), pp. 415-426 (2014).
[17] T. Jalal, Some new I-lacunary generalized difference sequence spaces defined in n−normed spaces, Springer Proc. Math. Stat., 171, pp. 249-258, (2016).
[18] P.K. Kamthan, M. Gupta, Sequence spaces and series 1st Edn., M. Dekker, New York, ISBN 0-8247-1224-2, pp. 298-300, (1981).
[19] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24(1), pp. 169-176, (1981).
[20] J. Lindenstrauss, L. Tzafriri, On orlicz sequence spaces, Israel J. Math., 10, pp. 379-390, (1971).
[21] A. Misiak, n−Inner product spaces, Math. Nachr., 140, pp. 299-319, (1989).
[22] M. Mursaleen, K. Raj and S. K. Sharma, Some spaces of differences and lacunary statistical convergence in n-normed space defined by sequence of orlicz functions, Miskolc Mathematical Notes, 16(1), pp. 283-304, (2015).
[23] M. Mursaleen, S. K. Sharma and A. Kilicman, Sequence spaces defined by musielak-orlicz function over n-normed spaces, Abs. and Appl. Anal. Vol. 2013, ID 364743, (2013).
[24] J. Musielak, Orlicz spaces and modular spaces, 1st Edn., Springer, New York, ISBN 3-5401-2706-2, pp. 33-112, (1983).
[25] K. Raj, A.K. Sharma and S.K. Sharma, A sequence space defined by musielak-orlicz functions, Int. Jou. Pure Appl. Math., 67, pp. 472-484, (2011).
[26] K. Raj, A.K. Sharma and S.K. Sharma, Some new sequence spaces defined by a sequence of modulus functions in n−normed spaces, Int. Jou. Math. Sci. Engg. Appl., 5, pp. 395-403, (2011).
[27] A. Sahiner, M. Gurdal and F.K. Duden , Triple sequences and their statistical convergence, Selcuk Jou. Appl. Math., 8, pp. 49-55, (2007).
[28] A. Sahiner, B.C. Tripathy , Some I related properties of triple sequences, Selcuk Jou. Appl. Math., 9, pp. 9-18, (2008).
[29] E. Savas, On some new sequence spaces in 2-normed spaces using ideal convergence and an orlicz function, Jou. Ineq. Appl., Vol. 2010, ID 482392, (2010).
[30] A. Wilansky, Modern methods in topological vector spaces, McGrawHill, ISBN-0-07-070180-6, (1978).
Publicado
2018-09-25
Cómo citar
Jalal, T., & Ahmad, I. (2018). Some new triple sequence spaces over n-normed space. Proyecciones. Journal of Mathematics, 37(3), 547-564. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/3170
Sección
Artículos