دانشگاه شهید مدنی آذربایجان

 آمار

تعداد نشریات6
تعداد شماره‌ها126
تعداد مقالات1,591
تعداد مشاهده مقاله1,806,299
تعداد دریافت فایل اصل مقاله1,673,835
Prasad, Kalika, Kumari, Munesh, Kızılateş, Can. (1403). Some properties and identities of hyperbolic generalized k-Horadam quaternions and octonions. , 9(4), 707-724. doi: 10.22049/cco.2023.28272.1495
Kalika Prasad; Munesh Kumari; Can Kızılateş. "Some properties and identities of hyperbolic generalized k-Horadam quaternions and octonions". , 9, 4, 1403, 707-724. doi: 10.22049/cco.2023.28272.1495
Prasad, Kalika, Kumari, Munesh, Kızılateş, Can. (1403). 'Some properties and identities of hyperbolic generalized k-Horadam quaternions and octonions', , 9(4), pp. 707-724. doi: 10.22049/cco.2023.28272.1495
Prasad, Kalika, Kumari, Munesh, Kızılateş, Can. Some properties and identities of hyperbolic generalized k-Horadam quaternions and octonions. , 1403; 9(4): 707-724. doi: 10.22049/cco.2023.28272.1495

Some properties and identities of hyperbolic generalized k-Horadam quaternions and octonions

Communications in Combinatorics and Optimization
مقاله 7، دوره 9، شماره 4، اسفند 2024، صفحه 707-724    اصل مقاله (444.23 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2023.28272.1495
نویسندگان
Kalika Prasad1؛ Munesh Kumari* 1؛ Can Kızılateş2
1Department of Mathematics, Central University of Jharkhand, 835205, India
2Department of Mathematics, Zonguldak Bülent Ecevit University, 67100, Turkey
چکیده
The aim of this paper is to introduce the hyperbolic generalized $k$-Horadam quaternions and octonions and investigate their algebraic properties. We present some properties and identities of these quaternions and octonions for generalized $k$-Horadam numbers. Moreover, we give some determinants related to the hyperbolic generalized $k$-Horadam quaternions and octonions. Finally, we evaluate its determinants through the Chebyshev polynomials of the second kind and give an illustrative example as well.
کلیدواژه‌ها
Horadam number؛ Hyperbolic quaternions and octonions؛ Binet formula؛ Generating Function؛ Chebyshev polynomials
مراجع
[1] J. Baez, The octonions, Bull. Amer. Math. Soc. 39 (2002), no. 2, 145–205.

[2] D. Bród, A. Szynal-Liana, and I. Wloch, On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Math. Methods Appl. Sci. 44 (2021), no. 6, 4607–4615.  https://doi.org/10.1002/mma.7054

[3] A. Cariow and G. Cariowa, An unified approach for developing rationalized algorithms for hypercomplex number multiplication, Electric Review 91 (2015), no. 2, 36–39.  https://doi.org/10.15199/48.2015.02.09

[4] A. Cariow, G. Cariowa, and J. Knapinski, Derivation of a low multiplicative complexity algorithm for multiplying hyperbolic octonions, arXiv:1502.06250, 2015.  https://doi.org/10.48550/arXiv.1502.06250

[5] P. Catarino, A note on certain matrices with $h(x)$–Fibonacci quaternion polynomials, J. Difference Equ. Appl. 22 (2016), no. 2, 343–351.  https://doi.org/10.1080/10236198.2015.1092526

[6] J.H. Conway and D.A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, AK Peters/CRC Press, 2003.

[7] S. Falcon, On the generating matrices of the $k$-Fibonacci numbers, Proyecciones (Antofagasta) 32 (2013), no. 4, 347–357.  http://dx.doi.org/10.4067/S0716–09172013000400004

[8] R. Frontczak, A short remark on Horadam identities with binomial coefficients, Ann. Math. Inform., vol. 54, Eszterházy Károly Egyetem Líceum Kiadó, 2021, pp. 5–13.  http://doi.org/10.33039/ami.2021.03.016

[9] A.D. Godase, Hyperbolic $k$-Fibonacci and $k$-Lucas octonions, Notes Number Theory Discrete Math. 26 (2020), no. 3, 176–188.  http://doi.org/10.7546/nntdm.2020.26.3.176-188

[10] A.D. Godase, Hyperbolic $k$-Fibonacci and $k$-Lucas quaternions, The Mathematıcs Student 90 (2021), no. 1-2, 103–116.

[11] S. Halici and A. Karataş, On a generalization for Fibonacci quaternions, Chaos, Solitons & Fractals 98 (2017), 178–82.  https://doi.org/10.1016/j.chaos.2017.03.037

[12] W.R. Hamilton, Elements of Quaternions, Longmans, Green, & Company, 1866.

[13] A.F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly 68 (1961), no. 5, 455–459. https://doi.org/10.2307/2311099

[14] A.F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), no. 3, 289–291.  https://doi.org/10.2307/2313129

[15] T. Horzum and E.G. Kocer, On some properties of Horadam polynomials, Int. Math. Forum, vol. 4, 2009, pp. 1243–1252.

[16] O. Keçilioğlu and I. Akkus, The Fibonacci octonions, Advances in Applied Clifford Algebras 25 (2015), no. 1, 151–158. https://doi.org/10.1007/s00006-014-0468-y

[17] C Kızılateş, On quaternions with incomplete Fibonacci and Lucas components, Util. Math. 110 (2019), 263–269.

[18] C. Kizilateş, A note on Horadam hybrinomials, Fundamental J. Math. Appl. 5 (2022), no. 1, 1–9.  https://doi.org/10.33401/fujma.993546

[19] C. Kızılate¸s, P. Catarino, and N. Tu˘glu, On the bicomplex generalized Tribonacci quaternions, Mathematics 7 (2019), no. 1, Article ID: 80.  https://doi.org/10.3390/math7010080

[20] C. Kizilateş and T. Kone, On higher order Fibonacci quaternions, The J. Analysis 29 (2021), no. 4, 1071–1082.

 [21] C. Kızılateş and E. Polatlı, New families of Fibonacci and Lucas octonions with $q$-integer components, Indian J. Pure Appl. Math. 52 (2021), no. 1, 231–240.  https://doi.org/10.1007/s13226-021-00073-0

[22] M. Kumari, K. Prasad, and H. Mahato, On $k$-Mersenne and $k$-Mersenne-Lucas octonions, arXiv:2207.12243, 2022 https://doi.org/10.48550/arXiv.2207.12243

[23] D.W. Niu, W.H. Li, and F. Qi, On signs of several Toeplitz–Hessenberg determinants whose elements contain central Delannoy numbers, Commun. Comb. Optim. 8 (2023), no. 4, 665–671.  https://doi.org/10.22049/CCO.2022.27707.1324

[24] E. Özkan, M. Uysal, and A.D. Godase, Hyperbolic $k$-Jacobsthal and $k$-Jacobsthal-Lucas quaternions, Indian J. Pure Appl. Math. 53 (2022), no. 4, 956–967.  https://doi.org/10.1007/s13226-021-00202-9

[25] E. Polatlı, A generalization of Fibonacci and Lucas quaternions, Adv. Appl. Clifford Algebr. 26 (2016), no. 2, 719–730. https://doi.org/10.1007/s00006-015-0626-x

[26] K. Prasad and H. Mahato, Cryptography using generalized Fibonacci matrices with Affine-Hill cipher, J. Discrete Math. Sci. Cryptogr. 25 (2022), no. 8, 2341–2352.  https://doi.org/10.1080/09720529.2020.1838744

[27] K. Prasad, H. Mahato, and M. Kumari, On the generalized $k$-Horadam-like sequences, Algebra, Analysis, and Associated Topics, Trends in Mathematics, Birkhäuser, Cham, 2022, pp. 11–26.

[28] G.Y. Şentürk, N. Gürses, and S. Yüce, Fundamental properties of extended Horadam numbers, Notes Number Theory Discret. Math. 27 (2021), no. 4, 219–235.  https://doi.org/10.7546/nntdm.2021.27.4.219-235

[29] T.D. Şentürk, . Bilgici, A. Daşdemir, and Z. Ünal, A study on Horadam hybrid numbers, Turkish J. Math. 44 (2020), no. 4, 1212–1221.  https://doi.org/10.3906/mat-1908-77

[30] G. Udrea, A note on the sequence $(W_n)_{n≥0}$ of A.F. Horadam, Portugaliae Math. 53 (1996), no. 2, 143–156.

[31] M. Uysal, M. Kumari, B. Kuloğlu, K. Prasad, and E. Özkan, On the hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas octonions, Kragujevac J. Math. 49 (2025), no. 5, 765–779.

[32] Y. Yazlik and N. Taskara, A note on generalized $k$-Horadam sequence, Comput. Math. Appl. 63 (2012), no. 1, 36–41. https://doi.org/10.1016/j.camwa.2011.10.055

[33] F. Yılmaz and M. Özkan, On the generalized Gaussian fibonacci numbers and Horadam hybrid numbers: A unified approach, Axioms 11 (2022), no. 6, Article ID: 255.  https://doi.org/10.3390/axioms11060255

آمار
تعداد مشاهده مقاله: 874
تعداد دریافت فایل اصل مقاله: 2,213


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب