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


Abstract views: 175 / PDF downloads: 207

Authors

DOI:

https://doi.org/10.26900/jsp.3.003

Keywords:

Orlicz function, difference space, completeness, solid space, symmetric space

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.

Downloads

Download data is not yet available.

References

1. Basarir, M. and Sonalcan, O.: On some double sequence spaces; J. Indian Acad. Math. 21(2), (1999); 193-200.
2. Bromwich T.J.IA: An Introduction to the Theory of Infinite Series; MacMillan and Co. Ltd. New york (1965).
3. Esi, A.: Some new sequence spaces defined by Orlicz functions; Bull. Inst. Math. Acad. Sinica.; 27(1) (1999), 71-76.

4. 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.
5. Et, M.: On some new Orlicz sequence spaces; J. Analysis; 9 (2001), 21-28.
6. Hardy G.H.: On the convergence of certain multiple series; Proc. Camb. Phil. Soc.; 19 (1917).
7. Kamthan, P.K. and Gupta, M.: Sequence Spaces and Series: Marcel Dekker, 1980.
8. Kizmaz, H: On certain sequence spaces; Canad. Math. Bull., 24 (1981), 169 –176.
9. Krasnoselkii, M.A. and Rutitsky, Y.B.: Convex function and Orlicz Spaces; Groningen Netherlands, 1961.
10. Lindenstrauss, J. and Tzafriri, L.: On Orlicz sequence spaces: Israel J. Math. 10 (1971), 379-390.
11. Maddox, I.J.: Spaces of strongly summable sequences. Quart. Jour. Math. (Oxford 2nd Ser), vol. 18, no.72(1976), 345-355.
12. Moricz, F: Extension of the spaces c and c0 from single to double sequences; Acta. Math. Hungerica.; 57(1-2), (1991), 129 -136.
13. 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.
14. Nakano H.: Modular sequence spaces; Proc. Japan Acad.; 27 (1951) , 508 – 512.
15. Simons, S.: The sequence spaces l(p) and m(p). Proc. London Math. Soc.,(3) 15 (1965), 422-436.
16. 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.
17. Tripathy B.C. and Sarma B.: Statistically convergent double sequence spaces defined by Orlicz functions; Soochow J. Math.; 32(2)(2006), 211-221.
18. Tripathy B.C., Choudhury B. and Sarma B.: Some Difference Double Sequence Spaces Defined By Orlicz Function, Kyungpook Math. J. 48(2008), 613-622.
19. Zygumd, A.: Trigonometric Series, vol II , Cambridge (1993) .

Downloads

Published

2019-01-31

How to Cite

SARMA, B. (2019). SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION. HEALTH SCIENCES QUARTERLY, 3(1), 21–28. https://doi.org/10.26900/jsp.3.003

Issue

Vol. 3 No. 1 (2019)

Section

Letter to the Editor

License

When the  article is accepted for publication in the HSQ authors transfer all copyright in the article to the Holistence Academy Ar-Ge Yazılım Yayıncılık Eğitim Danışmanlık ve Organizasyon Ticaret Ltd. Şti.The authors reserve all proprietary right other than copyright, such as patent rights. 

Everyone who is listed as an author in this article should have made a substantial, direct, intellectual contribution to the work and should take public responsibility for it.

This paper contains works that have not previously published or not under consideration for publication in other journals.