Year 2023,
Volume: 6 Issue: 4, 211 - 225, 25.12.2023
Uskan Devletli
Merve Ilkhan Kara
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
Uskan Devletli
Merve Ilkhan Kara
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.