On paranorm \(BV_\sigma\) I-convergent sequence spaces defined by an Orlicz function

  • Authors

    • Vakeel.A. Khan
    • Ayhan Esi Adiyaman University, Science and Art Faculty, Department of Mathematics, 02040, Adiyaman, Turkey
    • Mohd Shafiq
    2014-03-16
    https://doi.org/10.14419/gjma.v2i2.2162
  • Bounded variation, Invariant mean, \(\sigma\)-Bounded variation, Ideal, Filter, Orlicz function, I-convergence, I-null, Solid space, Sequence algebra, paranorm.
  • In this article we introduce and study \(_{0}BV^I_\sigma(M,p)\), \(BV^I_{\sigma}(M,p)\) and \(_{\infty}BV^I_{\sigma}(M,p)\) sequence spaces where \(p=(p_{k})\) is the sequence of strictly positive real numbers with the help of \(BV_\sigma\) space [see [23]] and an Orlicz function \(M\). We study some topological and algebraic properties and decompostion theorem. Further we prove some inclusion relations related to these new spaces.

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    Khan, V., Esi, A., & Shafiq, M. (2014). On paranorm \(BV_\sigma\) I-convergent sequence spaces defined by an Orlicz function. Global Journal of Mathematical Analysis, 2(2), 28-43. https://doi.org/10.14419/gjma.v2i2.2162