Some new triple sequence spaces over n-normed space.

• Jalal, Tanweer ^[1] ; Ahmad, Ishfaq ^[1]
  1. [1] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 3, 2018, págs. 547-564
• Idioma: inglés
• DOI: 10.4067/s0716-09172018000300547
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • A. Alotaibi, M. Mursaleen and S. K. Sharma, Double sequence spaces over n-normed spaces defined by a sequence of orlicz functions, Jou. Ineq....
  • A. J. Datta, A. Esi and B.C. Tripathy, Statistically convergent triple sequence space defined by orlicz function, Jou. Math. Anal., 4, pp....
  • S. Debnath, B.C. Sarma Das, Some generalized triple sequence spaces of real numbers, Jou. Nonl. Anal. and Opt., 6, pp. 71-79, (2015).
  • H. Dutta, An application of lacunary summability method to n-norm, Int. Jou. Appl. Math. Sat., 15 (D09), pp. 89-97, (2009).
  • 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).
  • H. Dutta, On some n-normed linear space valued difference sequence, Jou. Franklin Inst., 348, pp. 2876-2883, (2011).
  • A. Esi, On some triple almost lacunary sequence spaces defined by orlicz functions, Research and Reviews: Discrete Mathematical structures...
  • A. Esi, M.N. Catalbas, Almost convergence of triple sequences, G. Jou. Math. Anal., 2, pp. 6-10, (2014).
  • A. Esi, E. Savas, On lacunary statically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9, pp. 2529-2534,...
  • M. Et, R. Colak, On generalized difference sequence spaces, Soochow Jou. Math., 21, 4, pp. 377-386, (1995).
  • S. Gähler, Linear 2-normietre rume, Math. Nachr., 28, pp. 1-43, (1965).
  • H. Gunawan, On n−inner product, n−norms, and the cauchySchwartz Inequality, Sci. Math. Jap., 5, pp. 47-54, (2001).
  • H. Gunawan, The space of p−summable sequence and its natural n−norm, Bull. Austral. Math. Soc., 64, pp. 137-147, (2001).
  • H. Gunawan, M. Mashadi, On n−normed spaces, Int. Jou. Math. Sci., 27, pp. 631-639, (2001).
  • T. Jalal, Some new I-convergent sequence spaces defined by using a sequence of modulus functions in n−normed spaces, Int. Jou. Math. Archive,...
  • T. Jalal, On generalized A-difference sequence spaces defined by ideal convergence on a real n−normed space through lacunary sequences, Bull....
  • T. Jalal, Some new I-lacunary generalized difference sequence spaces defined in n−normed spaces, Springer Proc. Math. Stat., 171, pp. 249-258,...
  • P.K. Kamthan, M. Gupta, Sequence spaces and series 1st Edn., M. Dekker, New York, ISBN 0-8247-1224-2, pp. 298-300, (1981).
  • H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24(1), pp. 169-176, (1981).
  • J. Lindenstrauss, L. Tzafriri, On orlicz sequence spaces, Israel J. Math., 10, pp. 379-390, (1971).
  • A. Misiak, n−Inner product spaces, Math. Nachr., 140, pp. 299-319, (1989).
  • M. Mursaleen, K. Raj and S. K. Sharma, Some spaces of differences and lacunary statistical convergence in n-normed space defined by sequence...
  • M. Mursaleen, S. K. Sharma and A. Kilicman, Sequence spaces defined by musielak-orlicz function over n-normed spaces, Abs. and Appl. Anal....
  • J. Musielak, Orlicz spaces and modular spaces, 1st Edn., Springer, New York, ISBN 3-5401-2706-2, pp. 33-112, (1983).
  • 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).
  • 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....
  • A. Sahiner, M. Gurdal and F.K. Duden , Triple sequences and their statistical convergence, Selcuk Jou. Appl. Math., 8, pp. 49-55, (2007).
  • A. Sahiner, B.C. Tripathy , Some I related properties of triple sequences, Selcuk Jou. Appl. Math., 9, pp. 9-18, (2008).
  • 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,...
  • A. Wilansky, Modern methods in topological vector spaces, McGrawHill, ISBN-0-07-070180-6, (1978).