Upper Bound of Difference Operator on Some Matrix Domains

Lotfollah Karimi; Maryam Sinaei

doi:10.33187/jmsm.828002

EN

Upper Bound of Difference Operator on Some Matrix Domains

Abstract

In this study, we investigate the norm of difference operator on some sequence spaces such as Hilbert and Cesaro matrix domains. Therefore the present study is a complement for those results obtained in [1].

Keywords

Difference operator, Hilbert matrix, Cesàro matrix, norm, sequence space

References

[1] H. Roopaei, D. Foroutannia, The norm of backward difference operator Dn on certain sequence spaces, Oper. Matrices, 12(3) (2018), 867-880.
[2] H. Roopaei, Norm of Hilbert operator on sequence spaces, J. Inequal. Appl., 2020(117), (2020).
[3] H. Kizmaz, On certain sequence spaces I, Canad. Math. Bull., 25(2) (1981), 169-176.
[4] B. Altay, F. Basar, The fine spectrum and the matrix domain of the difference operator D on the sequence space `p, (0 < p < 1), Commun. Math. Anal., 2(2) (2007), 1–11.
[5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J., 55(1) (2003), 136–147.
[6] C. P. Chen, D. C. Luor, Z. y. Ou, Extensions of Hardy inequality, J. Math. Anal. Appl., 273 (2002), 160–171.
[7] B. Altay, F. Basar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl., 336(1) (2007), 632–645.
[8] E. E. Kara, M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208-2223.
[9] F. Basar, Domain of the composition of some triangles in the space of p-summable sequences, AIP Conference Proceedings, 1611 (2014), 348–356.
[10] H. Roopaei, F Basar, On the spaces of Cesaro absolutely p-summable, null, and convergent sequences, Math. Methods Appl. Sci., 44(5) (2021), 3670-3685.

[11] H. Roopaei, T. Yaying, Quasi-Cesaro matrix and associated sequence spaces, Turk. J. Math., 45(1) (2021), 153-166.
[12] H. Roopaei, M. ˙Ilkhan, Fractional Ces`aro matrix and its associated sequence space, Concr. Oper., 8(1), (2021), 24-39.
[13] M. ˙Ilkhan, E. E. Kara, A new Banach space defined by Euler totient matrix operator, Oper. Matrices, 13(2) (2019), 527-544.
[14] F. Bas¸ar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, 2012.
[15] H. Roopaei, D. Foroutannia, The norm of matrix operators on Ces`aro weighted sequence space, Linear Multilinear Algebra, 67(1) (2019), 175-185.
[16] H. Roopaei, D. Foroutannia, The norms of certain matrix operators from `p spaces into `p(Dn) spaces, Linear Multilinear Algebra, 67(4) (2019), 767-776.
[17] H. Roopaei, Norms of summability and Hausdorff mean matrices on difference sequence spaces, Math. Inequal. Appl., 22(3) (2019), 983-987.
[18] H. Roopaei, A study on Copson operator and its associated sequence spaces, J. Inequal. Appl., 2020(120) (2020).
[19] H. Roopaei, A study on Copson operator and its associated sequence spaces II, J. Inequal. Appl., 2020(239) (2020).
[20] H. Roopaei, Bounds of operators on the Hilbert sequence space, Concr. Oper., 7 (2020), 155-165.
[21] H. Roopaei, Binomial operator as a Hausdorff operator of the Euler type, Constr. Math. Anal., 3(4) (2020), 165-177.
[22] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd edition, Cambridge University Press, Cambridge, 2001.
[23] Ng P-N, Lee P-Y, Cesaro sequence spaces of non-absolute type, Comment. Math. Prace Mat., 20(2) (1978), 429-433.
[24] M. Sengonul, F. Basar, Cesaro sequence spaces of non-absolute type which include the spaces c0 and c, Soochow J. Math., 31(1) (2005), 107-119.
[25] H. Roopaei, D. Foroutannia, M. Ilkhan, E. E. Kara, Cesaro Spaces and Norm of Operators on These Matrix Domains, Mediterr. J. Math., 17, 121 (2020).
[26] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc., 576 (1996).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Lotfollah Karimi ^*
0000-0002-4414-524X
Iran

Maryam Sinaei
0000-0002-4414-524X
Iran

Publication Date

April 30, 2021

Submission Date

November 18, 2020

Acceptance Date

April 6, 2021

Published in Issue

Year 2021 Volume: 4 Number: 1

DOI

https://doi.org/10.33187/jmsm.828002

IZ

https://izlik.org/JA52KU68ZX

APA

Karimi, L., & Sinaei, M. (2021). Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling, 4(1), 19-24. https://doi.org/10.33187/jmsm.828002

AMA

1.Karimi L, Sinaei M. Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling. 2021;4(1):19-24. doi:10.33187/jmsm.828002

Chicago

Karimi, Lotfollah, and Maryam Sinaei. 2021. “Upper Bound of Difference Operator on Some Matrix Domains”. Journal of Mathematical Sciences and Modelling 4 (1): 19-24. https://doi.org/10.33187/jmsm.828002.

EndNote

Karimi L, Sinaei M (April 1, 2021) Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling 4 1 19–24.

IEEE

[1]L. Karimi and M. Sinaei, “Upper Bound of Difference Operator on Some Matrix Domains”, Journal of Mathematical Sciences and Modelling, vol. 4, no. 1, pp. 19–24, Apr. 2021, doi: 10.33187/jmsm.828002.

ISNAD

Karimi, Lotfollah - Sinaei, Maryam. “Upper Bound of Difference Operator on Some Matrix Domains”. Journal of Mathematical Sciences and Modelling 4/1 (April 1, 2021): 19-24. https://doi.org/10.33187/jmsm.828002.

JAMA

1.Karimi L, Sinaei M. Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling. 2021;4:19–24.

MLA

Karimi, Lotfollah, and Maryam Sinaei. “Upper Bound of Difference Operator on Some Matrix Domains”. Journal of Mathematical Sciences and Modelling, vol. 4, no. 1, Apr. 2021, pp. 19-24, doi:10.33187/jmsm.828002.

Vancouver

1.Lotfollah Karimi, Maryam Sinaei. Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling. 2021 Apr. 1;4(1):19-24. doi:10.33187/jmsm.828002