Research Article
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Year 2023, , 211 - 225, 25.12.2023
https://doi.org/10.33434/cams.1313696

Abstract

References

  • [1] B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$, Inform. Sci., 176(10) (2006), 1450-1462.
  • [2] 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.
  • [3] F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, İstanbul, 2012.
  • [4] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 2013(38) (2013), 15 pages.
  • [5] M. Kirişci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl., 60 (2010), 1299-1309.
  • [6] M. Kirişci, Riesz type integrated and differentiated sequence spaces, Bull. Math. Anal. Appl., 7(2) (2015), 14-27.
  • [7] S. Demiriz, E. E. Kara, On compact operators on some sequence spaces related to matrix $B (r, s, t)$}, Thai J. Math., 14(3) (2016), 651-666.
  • [8] M. Mursaleen, A.K. Noman, On some new difference sequence spaces of non-absolute type, Math. Comput. Modelling, 52(3-4) (2010), 603-617.
  • [9] T. Yaying, B. Hazarika, On sequence spaces defined by the domain of a regular Tribonacci matrix, Math. Slovaca, 70(3) (2020), 697-706.
  • [10] P. Zengin Alp, A new paranormed sequence space defined by Catalan conservative matrix, Math. Methods Appl. Sci., 44(9) (2021), 7651-7658.
  • [11] T. Yaying, B. Hazarika, M. Mursaleen, On sequence space derived by the domain of $q$-Cesaro matrix in $\ell_p$ space and the associated operator ideal, J. Math. Anal. Appl., 493(1) (2021), 124453.
  • [12] M. İlkhan, E. E. Kara, Matrix transformations and compact operators on Catalan sequence spaces, J. Math. Anal. Appl., 498(1) (2021), 124925.
  • [13] T. Yaying, Paranormed Riesz difference sequence spaces of fractional order, Kragujevac J. Math., 46(2) (2022), 175-191.
  • [14] P. Zengin Alp, E. E. Kara, New Banach spaces defined by the domain of Riesz-Fibonacci matrix, Korean J. Math., 29(4) (2021), 665-677.
  • [15] M. İlkhan Kara, H. Roopaei, The Cesaro–Gamma operator and its associated sequence space, Adv. Oper. Theory, 6(3) (2021), 1-21.
  • [16] H. Roopaei, M. İlkhan Kara, Negative difference operator and its associated sequence space, Numer. Funct. Anal. Optim., 42(4) (2021), 480-496.
  • [17] H. Roopaei, M. İlkhan, Fractional Ces`aro matrix and its associated sequence space, Concr. Oper., 8(1) (2021), 24-39.
  • [18] M. İlkhan, E. E. Kara, A new Banach space defined by Euler totient matrix operator, Oper. Matrices, 13(2) (2019), 527-544.
  • [19] S. Demiriz, S. Erdem, Domain of Euler-totient matrix operator in the space $Li_p$, Korean J. Math., 28(2) (2020), 361-378.
  • [20] S. Demiriz, M. İlkhan, E. E. Kara, Almost convergence and Euler totient matrix, Ann. Funct. Anal., 11(3) (2020), 604-616.
  • [21] S. Erdem, S. Demiriz, 4-dimensional Euler-totient matrix operator and some double sequence spaces, Math. Sci. Appl. E-Notes, 8(2) (2020), 110-122.
  • [22] G. C. Hazar Güleç, Merve İlkhan, A new paranormed series space using Euler totient means and some matrix transformations, Korean J. Math., 28(2) (2020), 205-221.
  • [23] G. C. Hazar Güleç, Merve İlkhan, A new characterization of absolute summability factors, Commun. Optim. Theory, 2020 (2020), Article ID 15, 11 pages.
  • [24] M. İlkhan, Matrix domain of a regular matrix derived by Euler totient function in the spaces $c_0$ and $c$, Mediterr. J. Math., 17 (2020), Article number 27.
  • [25] M. İlkhan, G. C. Hazar Güleç, A study on absolute Euler totient series space and certain matrix transformations, Mugla J. Sci. Technol., 6(1) (2020), 112-119.
  • [26] M. İlkhan, S. Demiriz, E. E. Kara, A new paranormed sequence space defined by Euler totient matrix, Karaelmas Sci. Eng. J., 9(2) (2019), 277-282.
  • [27] M. İlkhan, Certain geometric properties and matrix transformations on a newly introduced Banach space, Fundam. J. Math. Appl., 3(1) (2020), 45-51.
  • [28] M. İlkhan, N. Şimşek, E. E. Kara, A new regular infinite matrix defined by Jordan totient function and its matrix domain in $\ell_p$, Math. Methods Appl. Sci., 44(9) (2021), 7622-7633.
  • [29] E. E. Kara, N. Şimşek, M. İlkhan Kara, On new sequence spaces related to domain of the Jordan totient matrix, S. A. Mohiuddine, B. Hazarika (editors), Sequence space theory with applications, New York, Chapman and Hall/CRC, 2022, pp. 1-19.
  • [30] M. İlkhan, E. E. Kara, F. Usta, Compact operators on the Jordan totient sequence spaces, Math. Methods Appl. Sci., 44(9) (2021), 7666-7675.
  • [31] M. İlkhan, M. A. Bayrakdar, A study on matrix domain of Riesz-Euler totient matrix in the space of $p$-absolutely summable sequences, Commun. Adv. Math. Sci., 4(1) (2021), 14-25.
  • [32] M. Stieglitz, H. Tietz, Matrix transformationen von folgenraumen eine ergebnis¨ubersicht, Math. Z., 154 (1977), 1-16.
  • [33] B. Altay, F. Başar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl., 336 (2007), 632–645.
  • [34] M. Kirişci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl., 60 (2010), 1299-1309.

New Banach Sequence Spaces Defined by Jordan Totient Function

Year 2023, , 211 - 225, 25.12.2023
https://doi.org/10.33434/cams.1313696

Abstract

In this study, a special lower triangular matrix derived by combining Riesz matrix and Jordan totient matrix is used to construct new Banach spaces. $\alpha-$,$\beta-$,$\gamma-$duals of the resulting spaces are obtained and some matrix operators are characterized.

References

  • [1] B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$, Inform. Sci., 176(10) (2006), 1450-1462.
  • [2] 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.
  • [3] F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, İstanbul, 2012.
  • [4] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 2013(38) (2013), 15 pages.
  • [5] M. Kirişci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl., 60 (2010), 1299-1309.
  • [6] M. Kirişci, Riesz type integrated and differentiated sequence spaces, Bull. Math. Anal. Appl., 7(2) (2015), 14-27.
  • [7] S. Demiriz, E. E. Kara, On compact operators on some sequence spaces related to matrix $B (r, s, t)$}, Thai J. Math., 14(3) (2016), 651-666.
  • [8] M. Mursaleen, A.K. Noman, On some new difference sequence spaces of non-absolute type, Math. Comput. Modelling, 52(3-4) (2010), 603-617.
  • [9] T. Yaying, B. Hazarika, On sequence spaces defined by the domain of a regular Tribonacci matrix, Math. Slovaca, 70(3) (2020), 697-706.
  • [10] P. Zengin Alp, A new paranormed sequence space defined by Catalan conservative matrix, Math. Methods Appl. Sci., 44(9) (2021), 7651-7658.
  • [11] T. Yaying, B. Hazarika, M. Mursaleen, On sequence space derived by the domain of $q$-Cesaro matrix in $\ell_p$ space and the associated operator ideal, J. Math. Anal. Appl., 493(1) (2021), 124453.
  • [12] M. İlkhan, E. E. Kara, Matrix transformations and compact operators on Catalan sequence spaces, J. Math. Anal. Appl., 498(1) (2021), 124925.
  • [13] T. Yaying, Paranormed Riesz difference sequence spaces of fractional order, Kragujevac J. Math., 46(2) (2022), 175-191.
  • [14] P. Zengin Alp, E. E. Kara, New Banach spaces defined by the domain of Riesz-Fibonacci matrix, Korean J. Math., 29(4) (2021), 665-677.
  • [15] M. İlkhan Kara, H. Roopaei, The Cesaro–Gamma operator and its associated sequence space, Adv. Oper. Theory, 6(3) (2021), 1-21.
  • [16] H. Roopaei, M. İlkhan Kara, Negative difference operator and its associated sequence space, Numer. Funct. Anal. Optim., 42(4) (2021), 480-496.
  • [17] H. Roopaei, M. İlkhan, Fractional Ces`aro matrix and its associated sequence space, Concr. Oper., 8(1) (2021), 24-39.
  • [18] M. İlkhan, E. E. Kara, A new Banach space defined by Euler totient matrix operator, Oper. Matrices, 13(2) (2019), 527-544.
  • [19] S. Demiriz, S. Erdem, Domain of Euler-totient matrix operator in the space $Li_p$, Korean J. Math., 28(2) (2020), 361-378.
  • [20] S. Demiriz, M. İlkhan, E. E. Kara, Almost convergence and Euler totient matrix, Ann. Funct. Anal., 11(3) (2020), 604-616.
  • [21] S. Erdem, S. Demiriz, 4-dimensional Euler-totient matrix operator and some double sequence spaces, Math. Sci. Appl. E-Notes, 8(2) (2020), 110-122.
  • [22] G. C. Hazar Güleç, Merve İlkhan, A new paranormed series space using Euler totient means and some matrix transformations, Korean J. Math., 28(2) (2020), 205-221.
  • [23] G. C. Hazar Güleç, Merve İlkhan, A new characterization of absolute summability factors, Commun. Optim. Theory, 2020 (2020), Article ID 15, 11 pages.
  • [24] M. İlkhan, Matrix domain of a regular matrix derived by Euler totient function in the spaces $c_0$ and $c$, Mediterr. J. Math., 17 (2020), Article number 27.
  • [25] M. İlkhan, G. C. Hazar Güleç, A study on absolute Euler totient series space and certain matrix transformations, Mugla J. Sci. Technol., 6(1) (2020), 112-119.
  • [26] M. İlkhan, S. Demiriz, E. E. Kara, A new paranormed sequence space defined by Euler totient matrix, Karaelmas Sci. Eng. J., 9(2) (2019), 277-282.
  • [27] M. İlkhan, Certain geometric properties and matrix transformations on a newly introduced Banach space, Fundam. J. Math. Appl., 3(1) (2020), 45-51.
  • [28] M. İlkhan, N. Şimşek, E. E. Kara, A new regular infinite matrix defined by Jordan totient function and its matrix domain in $\ell_p$, Math. Methods Appl. Sci., 44(9) (2021), 7622-7633.
  • [29] E. E. Kara, N. Şimşek, M. İlkhan Kara, On new sequence spaces related to domain of the Jordan totient matrix, S. A. Mohiuddine, B. Hazarika (editors), Sequence space theory with applications, New York, Chapman and Hall/CRC, 2022, pp. 1-19.
  • [30] M. İlkhan, E. E. Kara, F. Usta, Compact operators on the Jordan totient sequence spaces, Math. Methods Appl. Sci., 44(9) (2021), 7666-7675.
  • [31] M. İlkhan, M. A. Bayrakdar, A study on matrix domain of Riesz-Euler totient matrix in the space of $p$-absolutely summable sequences, Commun. Adv. Math. Sci., 4(1) (2021), 14-25.
  • [32] M. Stieglitz, H. Tietz, Matrix transformationen von folgenraumen eine ergebnis¨ubersicht, Math. Z., 154 (1977), 1-16.
  • [33] B. Altay, F. Başar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl., 336 (2007), 632–645.
  • [34] M. Kirişci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl., 60 (2010), 1299-1309.
There are 34 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Uskan Devletli This is me 0000-0001-9857-9513

Merve Ilkhan Kara 0000-0002-0831-1474

Early Pub Date December 21, 2023
Publication Date December 25, 2023
Submission Date June 13, 2023
Acceptance Date December 18, 2023
Published in Issue Year 2023

Cite

APA Devletli, U., & Ilkhan Kara, M. (2023). New Banach Sequence Spaces Defined by Jordan Totient Function. Communications in Advanced Mathematical Sciences, 6(4), 211-225. https://doi.org/10.33434/cams.1313696
AMA Devletli U, Ilkhan Kara M. New Banach Sequence Spaces Defined by Jordan Totient Function. Communications in Advanced Mathematical Sciences. December 2023;6(4):211-225. doi:10.33434/cams.1313696
Chicago Devletli, Uskan, and Merve Ilkhan Kara. “New Banach Sequence Spaces Defined by Jordan Totient Function”. Communications in Advanced Mathematical Sciences 6, no. 4 (December 2023): 211-25. https://doi.org/10.33434/cams.1313696.
EndNote Devletli U, Ilkhan Kara M (December 1, 2023) New Banach Sequence Spaces Defined by Jordan Totient Function. Communications in Advanced Mathematical Sciences 6 4 211–225.
IEEE U. Devletli and M. Ilkhan Kara, “New Banach Sequence Spaces Defined by Jordan Totient Function”, Communications in Advanced Mathematical Sciences, vol. 6, no. 4, pp. 211–225, 2023, doi: 10.33434/cams.1313696.
ISNAD Devletli, Uskan - Ilkhan Kara, Merve. “New Banach Sequence Spaces Defined by Jordan Totient Function”. Communications in Advanced Mathematical Sciences 6/4 (December 2023), 211-225. https://doi.org/10.33434/cams.1313696.
JAMA Devletli U, Ilkhan Kara M. New Banach Sequence Spaces Defined by Jordan Totient Function. Communications in Advanced Mathematical Sciences. 2023;6:211–225.
MLA Devletli, Uskan and Merve Ilkhan Kara. “New Banach Sequence Spaces Defined by Jordan Totient Function”. Communications in Advanced Mathematical Sciences, vol. 6, no. 4, 2023, pp. 211-25, doi:10.33434/cams.1313696.
Vancouver Devletli U, Ilkhan Kara M. New Banach Sequence Spaces Defined by Jordan Totient Function. Communications in Advanced Mathematical Sciences. 2023;6(4):211-25.

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