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Year 2023, Volume: 6 Issue: 4, 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, Volume: 6 Issue: 4, 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 Volume: 6 Issue: 4

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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