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On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number

Year 2018, Volume: 31 Issue: 2, 555 - 567, 01.06.2018

Abstract

In this paper, we study the spectral norms of the geometric circulant
matrices
and the symmetric geometric
circulant matrices  with the Tribonacci numbers and any complex numbers r.



 

References

  • [1] Solak, S., “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 160: 125-132, (2005).
  • [2] Kocer, EG, Mansour, T, Tuglu, N., “Norms of circulant and semicirculant matrices with Horadam's numbers”, Ars Combinatoria, 85: 353-359, (2007).
  • [3] Shen, S.Q, Cen, J.M., “On the bounds for the norms of circulant matrices with Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 216: 2891-2897, (2010).
  • [4] Bahsi, M., “On the norms of circulant matrices with the hyperharmonic numbers”, Journal of Mathematical Inequalities, 10: (2), 445-458, (2016).
  • [5] Bahsi, M. and Solak, S., “On the norms of circulant matrices with the hyper-Fibonacci and Lucas numbers”, Journal of Mathematical Inequalities,8: (4), 693-705, (2014).
  • [6] Kızılateş, C. and Naim, T., “On the bounds for the spectral norms of geometric circulant matrices”, Journal of Inequalities and Applications, 2016:312 (2016).
  • [7] Tuglu, N. and Kızılateş C., “On the norms of circulant and circulant matrices with the hyperharmonic Fibonacci numbers”, Journal of Inequalities and Applications, 2015: 253, (2015).
  • [8] Tuglu, N, Kızılateş, C, Kesim, S., “On the harmonic and hyperharmonic Fibonacci numbers”, Advances Difference Equations, 2015: 297, (2015).
  • [9] Tuglu, N. and Kızılateş, C., “On the norms of some special matrices with the harmonic Fibonacci numbers”, Gazi University Journal of Science 28: (3) 447-501, (2015).
  • [10] Yazlik, Y, Taskara, N., “On the norms of an circulant matrix with the generalized Horadam numbers”, Journal of Inequalities and Applications, 2013: 394, (2013).
  • [11] R.A. Horn, C.R. Johnson, “Matrix Analysis”, Cambridge University Press, Cambridge, UK, 1985.
  • [12] R.A. Horn, C.R. Johnson, “Topics in Matrix Analysis”, Cambridge University Press, 1991, 259-260.
  • [13] He, C, Ma, J, Zhang, K, Wang, Z., “The upper bound estimation on the spectral norm circulant matrices with the Fibonacci and Lucas numbers”, Journal of Inequalities and Applications, 2015: 72, (2015).
  • [14] Bahsi, M., “On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers”, TWWS Journal of Pure and Applied. Mathematics, 6: (1), 84-92, (2015).
  • [15] Jiang, Z. and Zhou, J., “A note on spectral norms of even-order circulant matrices”, Applied Mathematics and Computation, 250: 368-371, (2015).
  • [16] Sintunavarat, W., “The upper bound estimation for the spectral norm of circulant and symmetric circulant matrices with the Padovan sequence”, Journal of Nonlinear Science and its Applications, 9: 92-101, (2016).
  • [17] Li, J, Jiang, Z, Lu, F., “Determinants, Norms and spread of circulant matrices with Tribonacci and generalized Lucas numbers”, Abstract Applied Analysis, 2014, Article ID 381829 (2014).
  • [18] Rabinowitz, S., “Algorithmic manipulation of third-order linear recurrences”, The Fibonacci Quarterly, 34: (5), 34: 447-463, (1996).
  • [19] Tascı, D., “On quadrapell numbers and quadrapell polynomials”, Hacettepe Journal of Mathematics and Statistics, 38: (3), 265-275, (2009).
Year 2018, Volume: 31 Issue: 2, 555 - 567, 01.06.2018

Abstract

References

  • [1] Solak, S., “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 160: 125-132, (2005).
  • [2] Kocer, EG, Mansour, T, Tuglu, N., “Norms of circulant and semicirculant matrices with Horadam's numbers”, Ars Combinatoria, 85: 353-359, (2007).
  • [3] Shen, S.Q, Cen, J.M., “On the bounds for the norms of circulant matrices with Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 216: 2891-2897, (2010).
  • [4] Bahsi, M., “On the norms of circulant matrices with the hyperharmonic numbers”, Journal of Mathematical Inequalities, 10: (2), 445-458, (2016).
  • [5] Bahsi, M. and Solak, S., “On the norms of circulant matrices with the hyper-Fibonacci and Lucas numbers”, Journal of Mathematical Inequalities,8: (4), 693-705, (2014).
  • [6] Kızılateş, C. and Naim, T., “On the bounds for the spectral norms of geometric circulant matrices”, Journal of Inequalities and Applications, 2016:312 (2016).
  • [7] Tuglu, N. and Kızılateş C., “On the norms of circulant and circulant matrices with the hyperharmonic Fibonacci numbers”, Journal of Inequalities and Applications, 2015: 253, (2015).
  • [8] Tuglu, N, Kızılateş, C, Kesim, S., “On the harmonic and hyperharmonic Fibonacci numbers”, Advances Difference Equations, 2015: 297, (2015).
  • [9] Tuglu, N. and Kızılateş, C., “On the norms of some special matrices with the harmonic Fibonacci numbers”, Gazi University Journal of Science 28: (3) 447-501, (2015).
  • [10] Yazlik, Y, Taskara, N., “On the norms of an circulant matrix with the generalized Horadam numbers”, Journal of Inequalities and Applications, 2013: 394, (2013).
  • [11] R.A. Horn, C.R. Johnson, “Matrix Analysis”, Cambridge University Press, Cambridge, UK, 1985.
  • [12] R.A. Horn, C.R. Johnson, “Topics in Matrix Analysis”, Cambridge University Press, 1991, 259-260.
  • [13] He, C, Ma, J, Zhang, K, Wang, Z., “The upper bound estimation on the spectral norm circulant matrices with the Fibonacci and Lucas numbers”, Journal of Inequalities and Applications, 2015: 72, (2015).
  • [14] Bahsi, M., “On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers”, TWWS Journal of Pure and Applied. Mathematics, 6: (1), 84-92, (2015).
  • [15] Jiang, Z. and Zhou, J., “A note on spectral norms of even-order circulant matrices”, Applied Mathematics and Computation, 250: 368-371, (2015).
  • [16] Sintunavarat, W., “The upper bound estimation for the spectral norm of circulant and symmetric circulant matrices with the Padovan sequence”, Journal of Nonlinear Science and its Applications, 9: 92-101, (2016).
  • [17] Li, J, Jiang, Z, Lu, F., “Determinants, Norms and spread of circulant matrices with Tribonacci and generalized Lucas numbers”, Abstract Applied Analysis, 2014, Article ID 381829 (2014).
  • [18] Rabinowitz, S., “Algorithmic manipulation of third-order linear recurrences”, The Fibonacci Quarterly, 34: (5), 34: 447-463, (1996).
  • [19] Tascı, D., “On quadrapell numbers and quadrapell polynomials”, Hacettepe Journal of Mathematics and Statistics, 38: (3), 265-275, (2009).
There are 19 citations in total.

Details

Journal Section Mathematics
Authors

Can Kızılateş

Naim Tuglu

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 31 Issue: 2

Cite

APA Kızılateş, C., & Tuglu, N. (2018). On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science, 31(2), 555-567.
AMA Kızılateş C, Tuglu N. On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science. June 2018;31(2):555-567.
Chicago Kızılateş, Can, and Naim Tuglu. “On the Norms of Geometric and Symmetric Geometric Circulant Matrices With the Tribonacci Number”. Gazi University Journal of Science 31, no. 2 (June 2018): 555-67.
EndNote Kızılateş C, Tuglu N (June 1, 2018) On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science 31 2 555–567.
IEEE C. Kızılateş and N. Tuglu, “On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number”, Gazi University Journal of Science, vol. 31, no. 2, pp. 555–567, 2018.
ISNAD Kızılateş, Can - Tuglu, Naim. “On the Norms of Geometric and Symmetric Geometric Circulant Matrices With the Tribonacci Number”. Gazi University Journal of Science 31/2 (June 2018), 555-567.
JAMA Kızılateş C, Tuglu N. On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science. 2018;31:555–567.
MLA Kızılateş, Can and Naim Tuglu. “On the Norms of Geometric and Symmetric Geometric Circulant Matrices With the Tribonacci Number”. Gazi University Journal of Science, vol. 31, no. 2, 2018, pp. 555-67.
Vancouver Kızılateş C, Tuglu N. On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science. 2018;31(2):555-67.