690
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Some new classes of paranorm ideal convergent double sequences of sigma-bounded variation over n-normed spaces

, , , & | (Reviewing Editor)
Article: 1460029 | Received 24 Aug 2017, Accepted 23 Mar 2018, Published online: 25 Apr 2018

References

  • Ahmad, Z. U., & Mursaleen, M. (1988). An application of Banach limits. Proceedings of the American Mathematical Society, 103(1), 244–246.
  • Altinok, H., Altin, Y., & Isik, M. (2008). The sequence space BVσ(M,p,q,s) on seminormed spaces. Indian Journal of Pure and Applied Mathematics, 39(1), 49–58.
  • Fast, H. (1951). Sur la convergence statistique. Colloquium Mathematicum, 2, 241–244. (French)
  • Isik, M., Altin, Y., & Et, M. (2013). Some properties of the sequence space BVθ(M,p,q,s). Journal of Inequalities and Applications, 305, 8.
  • Gahler, S. (1964). Lineare 2–normierte Raume. (German). Mathematische Nachrichten, 28, 1–43.
  • Gunawan, H. (2001). On finite dimensional 2–normed spaces. Soochow Journal of Mathematics, 27(3), 321–329.
  • Gunawan, H., & Mashadi, M. (2001). On n–normed spaces. International Journal of Mathematics and Mathematical Sciences, 27(10), 631–639.
  • Gurdal, M. (2006). On ideal convergent sequences in 2–normed spaces. Thai Journal of Mathematics, 4(1), 85–91.
  • Gurdal, M., & Sahnier, A. (2014). Ideal convergence in n–normal spaces and some new sequence spaces via n–norm. Malaysian Journal of Fundamental and Applied Sciences, 4(1),
  • Khan, V. A. (2008). On a new sequence space defined by Orlicz functions. Faculty of Sciences. University of Ankara. S\’{e}ries A57(2), 25–33.
  • Khan, V. A., Esi, A. & Shafiq, M. (2014a). On paranorm BVσ \textit{I}–convergent sequence spaces defined by an Orlicz function. Global Journal of Mathematical Analysis, 2(2), 28–43.
  • Khan, V. A., Esi, A. & Shafiq, M. (2014b). On some BVσ \textit{I}–convergent sequence spaces defined by modulus function. Global Journal of Mathematical Analysis, 2(2), 17–27.
  • Khan, V.A., Fatima, H., Abdullah, S.A.A., & Khan, D.M. (2016). On a new (BVσ) I–convergent double sequence spaces. Theory and Applications of Mathematics \ & Computer Science, 6(2), 187–197.
  • Khan, V.A. & Tabassum, S. (2011). On some new double sequence spaces of invariant means defined by Orlicz functions. Communications Faculty of Sciences, 60(2), 11–21.
  • Kostyrko, P., Wilczynski, W., & Salat, T. (2000). \textit{I}--convergence. Real Analysis Exchange, 26(2), 669–686.
  • Lascarides, C. G. (1971). A study of certain sequence spaces of Maddox and a generalization of a theorem of Iyer. Pacific Journal of Mathematics, 38, 487–500.
  • Lascarides, C.G. (1983). On the equivalence of certain sets of sequences. Indian Journal of Mathematics, 25(1), 41–52.
  • Maddox, I. J. (1969). Some properties of paranormed sequence spaces. Journal of the London Mathematical Society, 1(2), 316–322.
  • Maddox, I.J. (1989). Elements of functional analysis (2nd edition). Cambridge: Cambridge University Press.
  • Misiak, A. (1989). \textit{n}–inner product spaces. Mathematische Nachrichten, 140, 299–319.
  • Mursaleen, M. (1983). On some new invariant matrix methods of summability. The Quarterly Journal of Mathematics, 34(133), 77–86.
  • Mursaleen, M., & Mohiuddine, S. A. (2010). Some new double sequence spaces of invariant means. Glasnik Matematicki Serija III, 45(65)((1)), 139–153.
  • Nakano, H. (1951). Modulared sequence spaces. Proceedings of the Japan Academy, 27, 508–512.
  • Parashar, S. D., & Choudhary, B. (1994). Sequence spaces defined by Orlicz functions. Indian Journal of Pure and Applied Mathematics, 25(4), 419–428.
  • Raimi, R. A. (1963). Invariant means and invariant matrix methods of summability. Duke Mathematical Journal, 30, 81–94.
  • Schaefer, P. (1972). Infinite matrices and invariant means. Proceedings of the American Mathematical Society, 36(1), 104–110.
  • Simons, S. (1965). The sequence spaces l(pv) and m(pv). Proceedings of the London Mathematical Society, 15(3), 422–436.
  • Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum, 2(1), 73–74.
  • wilansky, A. (1984). Summability through functional analysis. North-Holland Mathematics Studies. Amsterdam: North-Holland Publishing Co. 85. Notas de Matematica [Mathematical Notes]