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Year 2020, , 102 - 108, 29.09.2020
https://doi.org/10.32323/ujma.669276

Abstract

References

  • [1] M. Bahşi, S. Solak, On the norms of $\mathit{r}$–circulant matrices with the hyper-Fibonacci and Lucas numbers, J. Math. Inequal., 8(4) (2014) 693–705.
  • [2] M. Bahşi, On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers, TWMS J. Pure Appl. Math., 6(1) (2015), 84–92.
  • [3] M. Bahşi, On the norms of $\mathit{r}$–circulant matrices with the hyperharmonic numbers, J. Math. Inequal., 10(2) (2016), 445–458.
  • [4] G. Bilgici, Two generalizations of Lucas sequence, Appl. Math. Comput., 245 (2014), 526–538.
  • [5] M. Edson, O. Yayenie, A new generalization of Fibonacci sequence and extended Binet’s formula, INTEGERS, 9 (2009), 639–654.
  • [6] C. He, J. Ma, K. Zhang, Z. Wang, The upper bound estimation on the spectral norm of $\mathit{r}$-circulant matrices with the Fibonacci and Lucas numbers, J. Inequal. Appl., 2015 (2015), Article ID 72, 10 pages.
  • [7] R. Horn, C. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  • [8] Z. Jiang, Z. Zhou, A note on spectral norms of even-order $\mathit{r}$-circulant matrices, Appl. Math. Comput., 250 (2015), 368–371.
  • [9] C. Kızılateş, On the Quadra Lucas-Jacobsthal numbers, Karaelmas Fen ve Müh. Derg., 7(2) (2017), 619–621.
  • [10] C. Kızılateş, N. Tuğlu, On the bounds for the spectral norms of geometric circulant matrices, J. Inequal. Appl., 2016 (2016), Article ID 312, 15 pages.
  • [11] C. Kızılates¸, N. Tu˘glu, On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number, Gazi Univ. J. Sci., 31(2) (2018), 555–567.
  • [12] E. G. Koçer, T. Mansour, N. Tuğlu, Norms of circulant and semicirculant matrices with Horadams’s numbers, Ars Comb., 85 (2007), 353–359.
  • [13] C. Köme, Y. Yazlık, On the spectral norms of r-circulant matrices with the biperiodic Fibonacci and Lucas numbers, J. Inequal. Appl., 2017 (2017), Article ID 192, 12 pages.
  • [14] R. Mathias, The spectral norm of a nonnegative matrix, Linear Algebra Appl., 139 (1990), 269-284.
  • [15] B. Radicic, On k–circulant matrices (with geometric sequence), Quaest. Math., 39 (2016), 135-144.
  • [16] S. Q. Shen, J. M. Cen, On the bounds for the norms of $\mathit{r}$–circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput., 216 (2010), 2891–2897.
  • [17] S. Q. Shen, J. M. Cen, On the Spectral Norms of $\mathit{r}$-Circulant Matrices with the k -Fibonacci and k-Lucas Numbers, Int. J. Contemp. Math. Sci., 5(12) (2010), 569–578.
  • [18] B. Shi, The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers, J. Inequal. Appl., 2018 (2018), Article ID 14, 9 pages.
  • [19] W. Sintunavarat, The upper bound estimation for the spectral norm of $\mathit{r}$–circulant and symmetric $\mathit{r}$–circulant matrices with the Padovan sequence, J. Nonlinear Sci. Appl., 9 (2016), 92–101.
  • [20] S. Solak, On the norms of circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput., 160 (2005), 125–132.
  • [21] N. Tuğlu, C. Kızılates¸, On the norms of circulant and $\mathit{r}$–circulant matrices with the hyperharmonic Fibonacci numbers, J. Inequal. Appl., 2015 (2015), Article ID 253, 11 pages.
  • [22] N. Tuğlu, C. Kızılateş, On the norms of some special matrices with the harmonic Fibonacci numbers, Gazi Univ. J. Sci., 28(3) (2015), 497–501.
  • [23] N. Tuğlu, C. Kızılateş, S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, Adv. Difference Equ., 2015 (2015), Article ID 297, 12 pages.
  • [24] O. Yayenie, New identities for generalized Fibonacci sequences and new generalization of Lucas sequences, SEA Bull. Math., 36 (2012), 739–752.
  • [25] Y. Yazlık, N. Taşkara, On the norms of an r–circulant matrix with the generalized k–Horadam numbers, J. Inequal. Appl., 2013 (2013), Article ID 394, 8 pages.

On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers

Year 2020, , 102 - 108, 29.09.2020
https://doi.org/10.32323/ujma.669276

Abstract

In this study, we obtain upper and lower bounds for the spectral norms of the geometric circulant matrices with the bi--periodic Fibonacci numbers and bi--periodic Lucas numbers, respectively. Then we give some bounds for the spectral norms of Kronecker and Hadamard products of these matrices.                                                                                                                                                                                                                  

References

  • [1] M. Bahşi, S. Solak, On the norms of $\mathit{r}$–circulant matrices with the hyper-Fibonacci and Lucas numbers, J. Math. Inequal., 8(4) (2014) 693–705.
  • [2] M. Bahşi, On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers, TWMS J. Pure Appl. Math., 6(1) (2015), 84–92.
  • [3] M. Bahşi, On the norms of $\mathit{r}$–circulant matrices with the hyperharmonic numbers, J. Math. Inequal., 10(2) (2016), 445–458.
  • [4] G. Bilgici, Two generalizations of Lucas sequence, Appl. Math. Comput., 245 (2014), 526–538.
  • [5] M. Edson, O. Yayenie, A new generalization of Fibonacci sequence and extended Binet’s formula, INTEGERS, 9 (2009), 639–654.
  • [6] C. He, J. Ma, K. Zhang, Z. Wang, The upper bound estimation on the spectral norm of $\mathit{r}$-circulant matrices with the Fibonacci and Lucas numbers, J. Inequal. Appl., 2015 (2015), Article ID 72, 10 pages.
  • [7] R. Horn, C. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  • [8] Z. Jiang, Z. Zhou, A note on spectral norms of even-order $\mathit{r}$-circulant matrices, Appl. Math. Comput., 250 (2015), 368–371.
  • [9] C. Kızılateş, On the Quadra Lucas-Jacobsthal numbers, Karaelmas Fen ve Müh. Derg., 7(2) (2017), 619–621.
  • [10] C. Kızılateş, N. Tuğlu, On the bounds for the spectral norms of geometric circulant matrices, J. Inequal. Appl., 2016 (2016), Article ID 312, 15 pages.
  • [11] C. Kızılates¸, N. Tu˘glu, On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number, Gazi Univ. J. Sci., 31(2) (2018), 555–567.
  • [12] E. G. Koçer, T. Mansour, N. Tuğlu, Norms of circulant and semicirculant matrices with Horadams’s numbers, Ars Comb., 85 (2007), 353–359.
  • [13] C. Köme, Y. Yazlık, On the spectral norms of r-circulant matrices with the biperiodic Fibonacci and Lucas numbers, J. Inequal. Appl., 2017 (2017), Article ID 192, 12 pages.
  • [14] R. Mathias, The spectral norm of a nonnegative matrix, Linear Algebra Appl., 139 (1990), 269-284.
  • [15] B. Radicic, On k–circulant matrices (with geometric sequence), Quaest. Math., 39 (2016), 135-144.
  • [16] S. Q. Shen, J. M. Cen, On the bounds for the norms of $\mathit{r}$–circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput., 216 (2010), 2891–2897.
  • [17] S. Q. Shen, J. M. Cen, On the Spectral Norms of $\mathit{r}$-Circulant Matrices with the k -Fibonacci and k-Lucas Numbers, Int. J. Contemp. Math. Sci., 5(12) (2010), 569–578.
  • [18] B. Shi, The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers, J. Inequal. Appl., 2018 (2018), Article ID 14, 9 pages.
  • [19] W. Sintunavarat, The upper bound estimation for the spectral norm of $\mathit{r}$–circulant and symmetric $\mathit{r}$–circulant matrices with the Padovan sequence, J. Nonlinear Sci. Appl., 9 (2016), 92–101.
  • [20] S. Solak, On the norms of circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput., 160 (2005), 125–132.
  • [21] N. Tuğlu, C. Kızılates¸, On the norms of circulant and $\mathit{r}$–circulant matrices with the hyperharmonic Fibonacci numbers, J. Inequal. Appl., 2015 (2015), Article ID 253, 11 pages.
  • [22] N. Tuğlu, C. Kızılateş, On the norms of some special matrices with the harmonic Fibonacci numbers, Gazi Univ. J. Sci., 28(3) (2015), 497–501.
  • [23] N. Tuğlu, C. Kızılateş, S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, Adv. Difference Equ., 2015 (2015), Article ID 297, 12 pages.
  • [24] O. Yayenie, New identities for generalized Fibonacci sequences and new generalization of Lucas sequences, SEA Bull. Math., 36 (2012), 739–752.
  • [25] Y. Yazlık, N. Taşkara, On the norms of an r–circulant matrix with the generalized k–Horadam numbers, J. Inequal. Appl., 2013 (2013), Article ID 394, 8 pages.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Emrah Polatlı 0000-0002-2349-8978

Publication Date September 29, 2020
Submission Date January 2, 2020
Acceptance Date July 13, 2020
Published in Issue Year 2020

Cite

APA Polatlı, E. (2020). On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers. Universal Journal of Mathematics and Applications, 3(3), 102-108. https://doi.org/10.32323/ujma.669276
AMA Polatlı E. On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers. Univ. J. Math. Appl. September 2020;3(3):102-108. doi:10.32323/ujma.669276
Chicago Polatlı, Emrah. “On Geometric Circulant Matrices Whose Entries Are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers”. Universal Journal of Mathematics and Applications 3, no. 3 (September 2020): 102-8. https://doi.org/10.32323/ujma.669276.
EndNote Polatlı E (September 1, 2020) On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers. Universal Journal of Mathematics and Applications 3 3 102–108.
IEEE E. Polatlı, “On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers”, Univ. J. Math. Appl., vol. 3, no. 3, pp. 102–108, 2020, doi: 10.32323/ujma.669276.
ISNAD Polatlı, Emrah. “On Geometric Circulant Matrices Whose Entries Are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers”. Universal Journal of Mathematics and Applications 3/3 (September 2020), 102-108. https://doi.org/10.32323/ujma.669276.
JAMA Polatlı E. On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers. Univ. J. Math. Appl. 2020;3:102–108.
MLA Polatlı, Emrah. “On Geometric Circulant Matrices Whose Entries Are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers”. Universal Journal of Mathematics and Applications, vol. 3, no. 3, 2020, pp. 102-8, doi:10.32323/ujma.669276.
Vancouver Polatlı E. On Geometric Circulant Matrices Whose Entries are Bi-Periodic Fibonacci and Bi-Periodic Lucas Numbers. Univ. J. Math. Appl. 2020;3(3):102-8.

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