Research Article
BibTex RIS Cite

SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION

Year 2019, Volume: 3 Issue: 1, 21 - 28, 31.01.2019
https://doi.org/10.26900/jsp.3.003

Abstract

In this article we
introduce some kth order difference operator on some double sequences operated
by an Orlicz function. We introduce some sequence spaces and study different
properties of these spaces like completeness, solidity, symmetricity etc. We
establish some inclusion results among them.

References

  • Basarir, M. and Sonalcan, O.: On some double sequence spaces; J. Indian Acad. Math. 21(2), (1999); 193-200.
  • Bromwich T.J.IA: An Introduction to the Theory of Infinite Series; MacMillan and Co. Ltd. New york (1965).
  • Esi, A.: Some new sequence spaces defined by Orlicz functions; Bull. Inst. Math. Acad. Sinica.; 27(1) (1999), 71-76.
  • Esi, A. and Et, M.: Some new sequence spaces defined by a sequence of Orlicz functions; Indian J. Pure. Appl. Math.; 31(8) (2000), 967-972.
  • Et, M.: On some new Orlicz sequence spaces; J. Analysis; 9 (2001), 21-28.
  • Hardy G.H.: On the convergence of certain multiple series; Proc. Camb. Phil. Soc.; 19 (1917).
  • Kamthan, P.K. and Gupta, M.: Sequence Spaces and Series: Marcel Dekker, 1980.
  • Kizmaz, H: On certain sequence spaces; Canad. Math. Bull., 24 (1981), 169 –176.
  • Krasnoselkii, M.A. and Rutitsky, Y.B.: Convex function and Orlicz Spaces; Groningen Netherlands, 1961.
  • Lindenstrauss, J. and Tzafriri, L.: On Orlicz sequence spaces: Israel J. Math. 10 (1971), 379-390.
  • Maddox, I.J.: Spaces of strongly summable sequences. Quart. Jour. Math. (Oxford 2nd Ser), vol. 18, no.72(1976), 345-355.
  • Moricz, F: Extension of the spaces c and c0 from single to double sequences; Acta. Math. Hungerica.; 57(1-2), (1991), 129 -136.
  • Moricz, F. and Rhoades B.E.: Almost convergence of double sequences and strong regularity of summability matrices; Math. Proc. Camb. Phil. Soc.; 104 (1988), 283-294.
  • Nakano H.: Modular sequence spaces; Proc. Japan Acad.; 27 (1951) , 508 – 512.
  • Simons, S.: The sequence spaces l(p) and m(p). Proc. London Math. Soc.,(3) 15 (1965), 422-436.
  • Tripathy B.C.: Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex spaces; Soochow J. Math. 30(4)(2004), 431-446.
  • Tripathy B.C. and Sarma B.: Statistically convergent double sequence spaces defined by Orlicz functions; Soochow J. Math.; 32(2)(2006), 211-221.
  • Tripathy B.C., Choudhury B. and Sarma B.: Some Difference Double Sequence Spaces Defined By Orlicz Function, Kyungpook Math. J. 48(2008), 613-622.
  • Zygumd, A.: Trigonometric Series, vol II , Cambridge (1993) .
Year 2019, Volume: 3 Issue: 1, 21 - 28, 31.01.2019
https://doi.org/10.26900/jsp.3.003

Abstract

References

  • Basarir, M. and Sonalcan, O.: On some double sequence spaces; J. Indian Acad. Math. 21(2), (1999); 193-200.
  • Bromwich T.J.IA: An Introduction to the Theory of Infinite Series; MacMillan and Co. Ltd. New york (1965).
  • Esi, A.: Some new sequence spaces defined by Orlicz functions; Bull. Inst. Math. Acad. Sinica.; 27(1) (1999), 71-76.
  • Esi, A. and Et, M.: Some new sequence spaces defined by a sequence of Orlicz functions; Indian J. Pure. Appl. Math.; 31(8) (2000), 967-972.
  • Et, M.: On some new Orlicz sequence spaces; J. Analysis; 9 (2001), 21-28.
  • Hardy G.H.: On the convergence of certain multiple series; Proc. Camb. Phil. Soc.; 19 (1917).
  • Kamthan, P.K. and Gupta, M.: Sequence Spaces and Series: Marcel Dekker, 1980.
  • Kizmaz, H: On certain sequence spaces; Canad. Math. Bull., 24 (1981), 169 –176.
  • Krasnoselkii, M.A. and Rutitsky, Y.B.: Convex function and Orlicz Spaces; Groningen Netherlands, 1961.
  • Lindenstrauss, J. and Tzafriri, L.: On Orlicz sequence spaces: Israel J. Math. 10 (1971), 379-390.
  • Maddox, I.J.: Spaces of strongly summable sequences. Quart. Jour. Math. (Oxford 2nd Ser), vol. 18, no.72(1976), 345-355.
  • Moricz, F: Extension of the spaces c and c0 from single to double sequences; Acta. Math. Hungerica.; 57(1-2), (1991), 129 -136.
  • Moricz, F. and Rhoades B.E.: Almost convergence of double sequences and strong regularity of summability matrices; Math. Proc. Camb. Phil. Soc.; 104 (1988), 283-294.
  • Nakano H.: Modular sequence spaces; Proc. Japan Acad.; 27 (1951) , 508 – 512.
  • Simons, S.: The sequence spaces l(p) and m(p). Proc. London Math. Soc.,(3) 15 (1965), 422-436.
  • Tripathy B.C.: Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex spaces; Soochow J. Math. 30(4)(2004), 431-446.
  • Tripathy B.C. and Sarma B.: Statistically convergent double sequence spaces defined by Orlicz functions; Soochow J. Math.; 32(2)(2006), 211-221.
  • Tripathy B.C., Choudhury B. and Sarma B.: Some Difference Double Sequence Spaces Defined By Orlicz Function, Kyungpook Math. J. 48(2008), 613-622.
  • Zygumd, A.: Trigonometric Series, vol II , Cambridge (1993) .
There are 19 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Bipul Sarma This is me 0000-0003-4446-6710

Publication Date January 31, 2019
Published in Issue Year 2019 Volume: 3 Issue: 1

Cite

APA Sarma, B. (2019). SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION. Journal of Scientific Perspectives, 3(1), 21-28. https://doi.org/10.26900/jsp.3.003