On paranorm \(BV_\sigma\) I-convergent sequence spaces defined by an Orlicz function
DOI:
https://doi.org/10.14419/gjma.v2i2.2162Keywords:
Bounded variation, Invariant mean, \(\sigma\)-Bounded variation, Ideal, Filter, Orlicz function, I-convergence, I-null, Solid space, Sequence algebra, paranorm.Abstract
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.References
Z.U.Ahmad,M.Mursaleen : An application of Banach limits. Proc.Amer. Math. soc. 103,244-246,(1983).
S.Banach : Theorie des operations lineaires,Warszawa.(1932). 103,244-246(1986).
V. K. Bhardwaj and N., Singh: Some sequence spaces defined by Orlicz functions.Demonstratio Math. 33(3) (2000) 571582.
K. Demirci : I-limit superior and limit inferior.Math. Commun.,6:165-172(2001).
A. Esi:Some new sequence spaces defined by Orlicz functions, Bull. Inst. Math. Acad. Sinica. 27 (1999) 7176.
H.Fast:Sur la convergence statistique,Colloq.Math.2(1951),241-244.
J.A.Fridy:On statistical convergence,Analysis.5(1985).301-313.
B. Hazarika et al.:On paranormed Zweier ideal convergent sequence spaces defined By Orlicz function., Journal of the Egyptian Mathematical Society (2013), http://dx.doi.org/10.1016/j.joems.2013.08.005
P.K.Kamthan and M.Gupta : Sequence spaces and series.Marcel Dekker Inc,New York.(1980).
V.A. Khan :On a new sequence space defined by Orlicz Functions. Commun.Fac.Sci Univ.Ank.Series A1.57, 25-33,(2008).
V.A. Khan, K. Ebadullah, A.Esi, N. Khan, M. Shafiq:On paranorm Zweier I-convergent sequences spaces, Journal of Mathematics (Hindawi Publishing Corporation) Volume 2013 (2013), Article ID 613501, 6 pages
V.A Khan and K.Ebadullah :On some new I-convergent sequence space., Mathematics,Aeterna,Vol.3 No.2151-159(2013).
V.A.Khan and K. Ebadullah,K.:On a new I-convergent sequence space.Analysis,32, 199-208(2012).
J.P.King : Almost summable Sequences. Proc.Amer. Math. soc.17,1219-1225,(1966).
P.Kostyrko,M. Macaj and T. Salat :Statistical convergence and I-convergence.Real Analysis Exchange.
P.Kostyrko, T. Salat and W.Wilczynski :I-convergence,Raal Analysis Analysis Exchange.26(2),669-686(2000).
C.G.Lascarides:On the equivalence of certain sets of sequences,Indian J. Math. 25(1983),41-52.
J. Lindenstrauss and L. Tzafriri:On Orlicz sequence spaces, Israel J. Math. 101(1971) 379390.
G.G. Lorentz,: A contribution to the theory of divergent series. Acta Math.,80: 167-190(1948).
I.J.Maddox,: Elements of Functional Analysis,Cambridge University Press.(1970)
I.J. Maddox :Paranormed sequence spaces generated by infinite matrices., Math. Proc. Cambridge Philos. Soc. 64 (1968) 335340
M.Mursaleen: Matrix transformation between some new sequence spaces. Houston J. Math.,9: 505-509(1983).
M. Mursaleen: On some new invariant matrix methods of summability. Quart. J. Math. Oxford,(2)34: 77-86(1983).
H. Nakano: Modular sequence spaces., Proc. Jpn. Acad. Ser. A Math. Sci. 27 (1951) 508512.
S.D.Parshar and B.Choudhary:Sequence Spaces Defined by Orlicz function.Indian J,Pure Appl.Math.25.419-428(1994) spaces. Math. Vesnik. 49 (1997) 187196.
R.A.Raimi: Invariant means and invariant matrix methods of summability. Duke J. Math.,30: 81-94(1963).
T. Salat,B.C.Tripathy and M.Ziman: On some properties of I-convergence.Tatra Mt. Math. Publ.,28: 279-286(2004).
T. Salat B.C.Tripathy and M.Ziman: On I-convergence field. Ital.J.Pure Appl. Math.,17: 45-54(2005).
P.Schafer: Infinite matrices and Invariant means. Proc.Amer. Math. soc.36,104-110,(1972).
B.C.Tripathy and B.Hazarika: Paranorm I-convergent sequence spaces. Math. Slovaca.59(4):485-494(2009).
B.C. Tripathy, B. Hazarika:I-convergent sequence spaces associated with multiplier sequences, Math. Ineq. Appl. 11 (3) (2008) 543548.
B.C.Tripathy and B.Hazarika:Some I-Convergent sequence spaces defined by Orlicz function., Acta Mathematicae Applicatae Sinica.27(1)149-154.(2011)
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal''s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).