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

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.

Keywords

• Orlicz function,difference space,completeness,solid space,symmetric space etc..

Kaynakça

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) .