Some geometric properties of lacunary Zweier Sequence Spaces of order a.

• Tamang, Karan ^[1] ; Hazarika, Bipan ^[2]
  1. [1] North Eastern Regional Institute of Science and Technology

     North Eastern Regional Institute of Science and Technology

     India

     
  2. [2] Rajiv Gandhi University

     Rajiv Gandhi University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 35, Nº. 4, 2016, págs. 481-490
• Idioma: inglés
• DOI: 10.4067/S0716-09172016000400009
• Enlaces
  • Texto completo
• Resumen

  • In this paper we introduce a new sequence space using Zweier matrix operator and lacunary sequence of order a. Also we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space.

• Referencias bibliográficas
  • Citas [1] R. Colak, C. A. Bektas λ-statistical convergence of order α, Acta Math. Sci., 31 (3), pp. 953-959, (2011).
  • [2] R. Colak, Statistical Convergence of Order α, Modern Methods in Analysis and Its Applications, pp. 121-129. Anamaya Pub., New Delhi (2010).
  • [3] Y. A. Cui, H. Hudzik, On the Banach-Saks and weak Banach-Saks properties of some Bannach sequence spaces, Acta Sci. Math.(Szeged), 65,...
  • [4] J. Diestel, Sequence and Series in Banach spaces, in Graduate Texts in Math., Vol. 92, Springer-Verlag, (1984).
  • [5] A. Esi, A. Sapszoglu, On some lacunary σ-strong Zweier convergent sequence spaces, Romai J., 8 (2), pp. 61-70, (2012).
  • [6] M. Et, M. Cinar, M. Karaka¸ s, On λ-statistical convergence of order α of sequences of function, J. Inequa. Appl., 2013:204, (2013).
  • [7] M. Et, S. A. Mohiuddine, A. Alotaibi, On λ-statistical convergence and strongly λ-summable functions of order α, J. Inequa. Appl., 2013:469,...
  • [8] M. Et, V. Karakaya, A new difference sequence set of order α and its geometrical properties, Abst. Appl. Anal., Volume 2014, Article ID...
  • [9] M. Et, M. Karakas, Muhammed Cinar, Some geometric properties of a new modular space defined by Zweier operator, Fixed point Theory Appl.,...
  • [10] B. Hazarika, K. Tamang, B. K. Singh, Zweier ideal convergent sequence spaces defined by Orlicz function, The J. Math. Comp. Sci., 8 (3),...
  • [11] B. Hazarika, K. Tamang, B. K. Singh, On paranormed Zweier ideal convergent sequence spaces defined by Orlicz Function, J. Egypt. Math....
  • [12] Y. F. Karababa and A. Esi, On some strong Zweier convergent sequence spaces, Acta Univ. Apulensis, 29, pp. 9-15, (2012).
  • [13] M. Karakas, M. Et, V. Karakaya, Some geometric properties of a new difference sequence space involving lacunary sequences, Acta Math....
  • [14] V. A. Khan, K. Ebadullah, A. Esi, N. Khan, M. Shafiq, On Paranorm Zweier I-convergent sequences spaces, Inter. J. Anal., Vol. 2013, Article...
  • [15] V. A. Khan, K. Ebadullah, A. Esi, M. Shafiq, On some Zweier Iconvergent sequence spaces defined by a modulus function, Afr. Mat. DOI...
  • [16] V. A. Khan, A. H. Saifi, Some geometric properties of a generalized Cesáro Masielak-Orlicz sequence space, Thai J. Math., 1 (2), pp....
  • [17] V. A. Khan, Some geometric properties for N¨ orlund sequence spaces, Nonlinear Anal. Forum, 11(1), pp. 101-108, (2006).
  • [18] V. A. Khan, Some geometric properties of a generalized Ces´ aro sequence space, Acta Math. Univ. Comenian, 79 (1), pp. 1-8, (2010).
  • [19] V. A. Khan, Some geometrical properties of Riesz-Musielak-Orlicz sequence spaces, Thai J. Math., 8(3), pp. 565-574, (2010).
  • [20] V. A. Khan, Some geometrical properties of generalized lacunary strongly convergent sequence space, J. Math. Anal., 2(2), pp. 6-14, (2011).
  • [21] L. Leindler, Uber die la Vallee-Pousinsche Summierbarkeit Allgemeiner Orthogonalreihen. Acta Math. Acad. Sci. Hung., 16, pp. 375-387,...
  • [22] M. Mursaleen, R. Colak, M. Et, Some geometric inequalities in a new Banach sequence space, J. Ineq. Appl., Article ID 86757, 6, (2007).
  • [23] M. Mursaleen, V. A. Khan, Some geometric properties of a sequence space of Riesz mean, Thai J. Math., 2, pp. 165-171, (2004).
  • [24] M. Sëngonül, On the Zweier sequence space, Demonstratio Math. Vol.XL No. (1), pp. 181-196, (2007).
  • [25] A. Wilansky, Summability Theory and its Applications, North-Holland Mathematics Studies 85, Elsevier Science Publications, Amsterdam,...