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

Bipul Sarma

doi:10.26900/jsp.3.003

EN

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..

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) .

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

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

Publication Date

January 31, 2019

Submission Date

December 9, 2018

Acceptance Date

January 9, 2019

Published in Issue

Year 2019 Volume: 3 Number: 1

DOI

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

IZ

https://izlik.org/JA38DJ89SW

Cite

RIS / Bibtex

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

AMA

1.Sarma B. SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION. JSP. 2019;3(1):21-28. doi:10.26900/jsp.3.003

Chicago

Sarma, Bipul. 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.

EndNote

Sarma B (January 1, 2019) SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION. Journal of Scientific Perspectives 3 1 21–28.

IEEE

[1]B. Sarma, “SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION”, JSP, vol. 3, no. 1, pp. 21–28, Jan. 2019, doi: 10.26900/jsp.3.003.

ISNAD

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

JAMA

1.Sarma B. SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION. JSP. 2019;3:21–28.

MLA

Sarma, Bipul. “SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION”. Journal of Scientific Perspectives, vol. 3, no. 1, Jan. 2019, pp. 21-28, doi:10.26900/jsp.3.003.

Vancouver

1.Bipul Sarma. SOME HIGHER ORDER DIFFERENCE DOUBLE SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION. JSP. 2019 Jan. 1;3(1):21-8. doi:10.26900/jsp.3.003