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Upper Bound of Difference Operator on Some Matrix Domains

Yıl 2021, Cilt: 4 Sayı: 1, 19 - 24, 30.04.2021
https://doi.org/10.33187/jmsm.828002

Öz

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].

Kaynakça

  • [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).
Yıl 2021, Cilt: 4 Sayı: 1, 19 - 24, 30.04.2021
https://doi.org/10.33187/jmsm.828002

Öz

Kaynakça

  • [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).
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Lotfollah Karimi 0000-0002-4414-524X

Maryam Sinaei 0000-0002-4414-524X

Yayımlanma Tarihi 30 Nisan 2021
Gönderilme Tarihi 18 Kasım 2020
Kabul Tarihi 6 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 1

Kaynak Göster

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 Karimi L, Sinaei M. Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling. Nisan 2021;4(1):19-24. doi:10.33187/jmsm.828002
Chicago Karimi, Lotfollah, ve Maryam Sinaei. “Upper Bound of Difference Operator on Some Matrix Domains”. Journal of Mathematical Sciences and Modelling 4, sy. 1 (Nisan 2021): 19-24. https://doi.org/10.33187/jmsm.828002.
EndNote Karimi L, Sinaei M (01 Nisan 2021) Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling 4 1 19–24.
IEEE L. Karimi ve M. Sinaei, “Upper Bound of Difference Operator on Some Matrix Domains”, Journal of Mathematical Sciences and Modelling, c. 4, sy. 1, ss. 19–24, 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 (Nisan 2021), 19-24. https://doi.org/10.33187/jmsm.828002.
JAMA 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 ve Maryam Sinaei. “Upper Bound of Difference Operator on Some Matrix Domains”. Journal of Mathematical Sciences and Modelling, c. 4, sy. 1, 2021, ss. 19-24, doi:10.33187/jmsm.828002.
Vancouver Karimi L, Sinaei M. Upper Bound of Difference Operator on Some Matrix Domains. Journal of Mathematical Sciences and Modelling. 2021;4(1):19-24.

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