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Tytuł artykułu

On generalized Orlicz sequence spaces defined by double sequences

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Języki publikacji
EN
Abstrakty
EN
S.D. Parashar and B. Choudhary defined in 1994 certain paranorms for some Orlicz sequence spaces. Their ideas are applied later for topologization of various generalized Orlicz sequence spaces. The author determines in 2011 some alternative F-seminorms (which are also paranorms) for such spaces. In this paper these results are extended to generalized Orlicz sequence spaces defined via double sequences.
Rocznik
Tom
Strony
65--80
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Institute of Mathematics University of Tartu 50090 Tartu, Estonia
Bibliografia
  • [1] Bhardwaj V.K., Singh N., On some new spaces of lacunary strongly σ-con-vergent sequences defined by Orlicz functions, Indian J. Pure Appl. Math., 31 (2000), 1515-1526.
  • [2] Boos J., Classical and Modern Methods in Summability, Oxford University Press, Oxford, 2000.
  • [3] Colak R., Tripathy B.C., Et M., Lacunary strongly summable sequences and q-lacunary almost statistical convergence, Vietnam J. Math., 34(2006), 129-138.
  • [4] Ebadullah K., Difference sequence spaces of invariant mean defined by Orlicz function, Int. J. Math. Sci. Eng. Appl., 6(6)(2012), 101-110.
  • [5] Esi A., Generalized difference sequence spaces defined by Orlicz functions, Gen. Math., 17(2009), 53-66.
  • [6] Esi A., On some generalized difference sequence spaces of invariant means defined by a sequence of Orlicz functions, J. Comput. Anal. Appl., 11(2009), 524-535.
  • [7] Esi A., Et M., Some new sequence spaces defined by a sequence of Orlicz functions, Indian J. Pure Appl. Math., 31(2000), 967-972.
  • [8] Et M., On some new Orlicz sequence spaces, J. Anal., 9(2001), 21-28.
  • [9] Güngör M., Et M., Δr-strongly summable sequences defined by Orlicz functions, Indian J. Pure Appl. Math., 34(2003), 1141-1151.
  • [10] Işik M., Some classes of almost convergent paranormed sequence spaces defined by Orlicz functions, Demonstratio Math., 45(2012), 585-592.
  • [11] Kamthan P.K., Gupta M., Sequence Spaces and Series, Marcel Dekker, New York and Basel, 1981.
  • [12] Kolk E., Topologies in generalized Orlicz sequence spaces, Filomat, 25(2011), 191-211.
  • [13] Kolk E., On generalized sequence spaces defined by modulus functions, Acta Comment. Univ. Tartu. Math., 17(2013), 179-205.
  • [14] Kolk E., Raidjõe A., F-seminorms on generalized double sequence spaces defined by modulus functions, Proc. Est. Acad. Sci., 63(2014), 121-132.
  • [15] Lindenstrauss J., Tzafriri L., Classical Banach Spaces. I. Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete 92, Springer-Verlag, Berlin-New York, 1977.
  • [16] Musielak J., Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034, Springer-Verlag, Berlin-Heidelberg-New York-Tokio, 1983.
  • [17] Nuray F., Gülcü A., Some new sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 26(1995), 1169-1176.
  • [18] Parashar S.D., Choudhary B., Sequence spaces defined by a Orlicz functions, Indian J. Pure Appl. Math., 25(1994), 419-428.
  • [19] Raj K., On some generalized convergent lacunary sequence spaces defined by a Musielak-Orlicz function, Kumamoto J. Math., 26(2013), 9-22.
  • [20] Raj K., Sharma S.K., Lacunary sequence spaces defined by a Musielak-Orlicz function, Matematiche, 68(2013), 33-51.
  • [21] Savas E., Savas R., On some sequence spaces and lacunary σ-statistical convergence, Math. Comput. Appl., 8(2003), 165-172.
  • [22] Savas E., Savas R., Some λ-sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 34(2003), 1673-1680.
  • [23] Woo Y.T., On modular sequence spaces, Studia Math., 48(1973), 271-289.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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