Research Article

On the hyperbolic Horadam matrix functions

Volume: 51 Number: 6 December 1, 2022
EN

On the hyperbolic Horadam matrix functions

Abstract

In this study, we introduce a new class of the hyperbolic matrix functions which are called symmetrical hyperbolic Horadam sine and cosine matrix functions and we present some hyperbolic and recursive properties of these new matrix functions. In addition, we introduce quasi-sine Horadam matrix function and also define the matrix form of the metallic shofars that related to the hyperbolic Horadam sine and hyperbolic Horadam cosine matrix functions.

Keywords

References

  1. [1] A.H. Al-Mohy and N.J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM J. Matrix Anal. Appl. 31 (3), 970-989, 2009.
  2. [2] M. Bahşi and S. Solak, On the Hyperbolic Fibonacci Matrix Functions, TWMS J. App. Eng. Math. 8 (2), 454-465, 2018.
  3. [3] M. Bahşi and S. Solak, Hyperbolic Horadam functions, Gazi Univ. J. Sci 32 (3), 956-965, 2019.
  4. [4] V.W. De Spinadel, From the Golden Mean to Chaos, Nueva Libreria, 1998, second edition, Nobuko, 2004.
  5. [5] E. Defez, J. Sastre, J.J. Ibanez, and P.A. Ruiz, Matrix Functions Solving Coupled Differential Models, Math. Comput. Model. 50 (5,6), 831-839, 2009.
  6. [6] E. Defez, J. Sastre, J.J. Ibanez, and P.A. Ruiz, Computing Matrix Functions Arising in Engineering Models with Orthogonal Matrix Polynomials, Math. Comput. Model. 57 (7,8), 1738-1743, 2013.
  7. [7] E. Defez, J. Sastre, J.J. Ibáñez and J. Peinado, Solving engineering models using hyperbolic matrix functions, Appl. Math. Model. 40 (4), 2837-2844, 2016.
  8. [8] G.I. Hargreaves, and N.J. Higham, Efficient Algorithms for the Matrix Cosine and Sine, Numer. Algorithms 40, 383-400, 2005.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

December 1, 2022

Submission Date

March 23, 2022

Acceptance Date

June 2, 2022

Published in Issue

Year 2022 Volume: 51 Number: 6

APA
Bahşi, M., & Mersin, E. Ö. (2022). On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics, 51(6), 1550-1562. https://doi.org/10.15672/hujms.1092305
AMA
1.Bahşi M, Mersin EÖ. On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics. 2022;51(6):1550-1562. doi:10.15672/hujms.1092305
Chicago
Bahşi, Mustafa, and Efruz Özlem Mersin. 2022. “On the Hyperbolic Horadam Matrix Functions”. Hacettepe Journal of Mathematics and Statistics 51 (6): 1550-62. https://doi.org/10.15672/hujms.1092305.
EndNote
Bahşi M, Mersin EÖ (December 1, 2022) On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics 51 6 1550–1562.
IEEE
[1]M. Bahşi and E. Ö. Mersin, “On the hyperbolic Horadam matrix functions”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, pp. 1550–1562, Dec. 2022, doi: 10.15672/hujms.1092305.
ISNAD
Bahşi, Mustafa - Mersin, Efruz Özlem. “On the Hyperbolic Horadam Matrix Functions”. Hacettepe Journal of Mathematics and Statistics 51/6 (December 1, 2022): 1550-1562. https://doi.org/10.15672/hujms.1092305.
JAMA
1.Bahşi M, Mersin EÖ. On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics. 2022;51:1550–1562.
MLA
Bahşi, Mustafa, and Efruz Özlem Mersin. “On the Hyperbolic Horadam Matrix Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, Dec. 2022, pp. 1550-62, doi:10.15672/hujms.1092305.
Vancouver
1.Mustafa Bahşi, Efruz Özlem Mersin. On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics. 2022 Dec. 1;51(6):1550-62. doi:10.15672/hujms.1092305

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