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Hyper-Fibonacci and Hyper-Lucas Hybrinomials

Yıl 2022, Cilt: 10 Sayı: 2, 293 - 300, 31.10.2022

Efruz Özlem Mersin Mustafa Bahşi

Öz

The hybrid numbers which are accepted as a generalization of complex, hyperbolic and dual numbers, have attracted the attention of many researchers recently. In this paper hyper-Fibonacci and hyper-Lucas hybrinomials are defined. The recurrence relations, generation functions, as well as some algebraic and combinatoric properties are examined for newly defined hybrinomials.

Anahtar Kelimeler

Hybrinomials Hyper-Fibonacci numbers Hyper-Lucas numbers Polynomials

Kaynakça

  • [1] T. Koshy, Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs and Tracts, New York: Wiley 2001.
  • [2] G. Bilici, New generalization of Fibonacci and Lucas sequences, Applied Mathematical Sciences 8(19) (2014) 1429-1437.
  • [3] O. Yayenie, A note on generalized Fibonacci sequences, Applied Mathematics and Computation 217 (2011) 5603-5611.
  • [4] M. Edson and O. Yayenie, A new generalization of Fibonacci sequences and extended Binet’s formula, Integers 9(6) (2009) 639-654.
  • [5] S. Falcon, and A. Plaza, On the Fibonacci k-numbers, Chaos, Solitons and Fractals 32(5) (2007) 1615-1624.
  • [6] C. K¨ome, Y. Yazlık and V. Mathusudanan, A new generalization of Fibonacci and Lucas p- numbers, Journal of Computational Analysis and Applications 25(4) (2018) 667-669.
  • [7] A.F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly 68(5) (1961) 455-459.
  • [8] G.Y. Lee and S.G. Lee, A note on generalized Fibonacci numbers, The Fibonacci Quarterly 33(3) (1995) 273-278.
  • [9] A.A. O¨ cal, N. Tuglu and E. Altinis¸ik, On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation 170(1) (2005) 584-596.
  • [10] A. Dil and I. Mez˝o, A symmetric algorithm hyperharmonic and Fibonacci numbers, Applied Mathematics and Computation 206 (2008) 942-951.
  • [11] M. Bahs¸i, I. Mez˝o and S. Solak, A symmetric algorithm for hyper-Fibonacci and hyper-Lucas numbers, Annales Mathematicae et Informaticae 43 (2014) 19-27.
  • [12] E. Polatlı, Hybrid numbers with Fibonacci and Lucas hybrid number coefficients, Preprints (2020), 2020120349.
  • [13] G. Cerda-Morales, Investigation of generalized Fibonacci hybrid numbers and their properties, Applied Mathematics E-notes 21 (2021) 110-118.
  • [14] E.G. Koc¸er and H. Alsan, Generalized hybrid Fibonacci and Lucas p- numbers, Indian Journal of Pure and Applied Mathematics (2021). https://doi.org/10.1007/s13226-021-00201-w
  • [15] E. Polatlı, A note on ratios of Fibonacci hybrid and Lucas hybrid numbers, Notes on Number Theory and Discrete Mathematics 27(3) (2021) 73-78. doi:10.7546/nntdm.2021.27.3.73-78
  • [16] N. Yilmaz, More identities on Fibonacci and Lucas hybrid numbers, Notes on Number Theory and Discrete Mathematics, 27 (2), (2021) 159–167. https://doi.org/10.7546/nntdm.2021.27.2.159-167
  • [17] A.Szynal-Liana and I. Wloch, The Fibonacci hybrid numbers, Utilitas Mathematica, 110, 3–10, (2019).
  • [18] C. Kızılates¸, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons and Fractals, 130 (2020) 109449. https://doi.org/10.1016/j.chaos.2019.109449
  • [19] M. Asci and S. Aydinyuz, Generalized k-order Fibonacci and Lucas hybrid numbers, Journal of Information and Optimization Sciences 42(8) (2021) 1765-1782. https://doi.org/10.1080/02522667.2021.1946238
  • [20] A. Szynal-Liana and I. Wloch, Introduction to Fibonacci and Lucas hybrinomials, Complex Variables and Elliptic Equations 65(10) (2020) 1736-1747.
  • [21] A. Szynal-Liana and I. Wloch, Generalized Fibonacci-Pell hybrinomials, Online Journal of Analytic Combinatorics 15 (2020), 1-12.
  • [22] M. O¨ zdemir, Introduction to hybrid numbers, Advances in Applied Clifford Algebras 28(11) (2018). https://doi.org/10.1007/s00006-018-0833-3
  • [23] C. Kızılates¸ and T. Kone, On special spacelike hybrid numbers with Fibonacci divisor number components, Indian Journal of Pure and Applied Mathematics (2022). https://doi.org/10.1007/s13226-022-00252-7
  • [24] A. Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae General Algebra and Applications 38 (2018) 91-98. doi: 10.7151/dmgaa. 1287
  • [25] N. Kilic, Introduction to k- Horadam hybrid numbers, Kuwait Journal of Science (2021). https://doi.org/10.48129/kjs.14929
  • [26] C. Kızılates¸, A note on Horadam hybrinomials, Fundamental Journal of Mathematics and Applications 5(1) (2022) 1-9. https://doi.org/10.33401/fujma.993546
  • [27] E. Sevgi, The generalized Lucas hybrinomials with two variables, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70(2) (2021) 622-630. https://doi.org/10.31801/cfsuasmas.854761
  • [28] D. Dumont, Matrices d’Euler-Seidel, Seminaire Lotharingien de Combinatorie 1981, B05c.
  • [29] R.L. Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics, Addison Wesley 1993.

Yıl 2022, Cilt: 10 Sayı: 2, 293 - 300, 31.10.2022

Efruz Özlem Mersin Mustafa Bahşi

Öz

Kaynakça

  • [1] T. Koshy, Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs and Tracts, New York: Wiley 2001.
  • [2] G. Bilici, New generalization of Fibonacci and Lucas sequences, Applied Mathematical Sciences 8(19) (2014) 1429-1437.
  • [3] O. Yayenie, A note on generalized Fibonacci sequences, Applied Mathematics and Computation 217 (2011) 5603-5611.
  • [4] M. Edson and O. Yayenie, A new generalization of Fibonacci sequences and extended Binet’s formula, Integers 9(6) (2009) 639-654.
  • [5] S. Falcon, and A. Plaza, On the Fibonacci k-numbers, Chaos, Solitons and Fractals 32(5) (2007) 1615-1624.
  • [6] C. K¨ome, Y. Yazlık and V. Mathusudanan, A new generalization of Fibonacci and Lucas p- numbers, Journal of Computational Analysis and Applications 25(4) (2018) 667-669.
  • [7] A.F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly 68(5) (1961) 455-459.
  • [8] G.Y. Lee and S.G. Lee, A note on generalized Fibonacci numbers, The Fibonacci Quarterly 33(3) (1995) 273-278.
  • [9] A.A. O¨ cal, N. Tuglu and E. Altinis¸ik, On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation 170(1) (2005) 584-596.
  • [10] A. Dil and I. Mez˝o, A symmetric algorithm hyperharmonic and Fibonacci numbers, Applied Mathematics and Computation 206 (2008) 942-951.
  • [11] M. Bahs¸i, I. Mez˝o and S. Solak, A symmetric algorithm for hyper-Fibonacci and hyper-Lucas numbers, Annales Mathematicae et Informaticae 43 (2014) 19-27.
  • [12] E. Polatlı, Hybrid numbers with Fibonacci and Lucas hybrid number coefficients, Preprints (2020), 2020120349.
  • [13] G. Cerda-Morales, Investigation of generalized Fibonacci hybrid numbers and their properties, Applied Mathematics E-notes 21 (2021) 110-118.
  • [14] E.G. Koc¸er and H. Alsan, Generalized hybrid Fibonacci and Lucas p- numbers, Indian Journal of Pure and Applied Mathematics (2021). https://doi.org/10.1007/s13226-021-00201-w
  • [15] E. Polatlı, A note on ratios of Fibonacci hybrid and Lucas hybrid numbers, Notes on Number Theory and Discrete Mathematics 27(3) (2021) 73-78. doi:10.7546/nntdm.2021.27.3.73-78
  • [16] N. Yilmaz, More identities on Fibonacci and Lucas hybrid numbers, Notes on Number Theory and Discrete Mathematics, 27 (2), (2021) 159–167. https://doi.org/10.7546/nntdm.2021.27.2.159-167
  • [17] A.Szynal-Liana and I. Wloch, The Fibonacci hybrid numbers, Utilitas Mathematica, 110, 3–10, (2019).
  • [18] C. Kızılates¸, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons and Fractals, 130 (2020) 109449. https://doi.org/10.1016/j.chaos.2019.109449
  • [19] M. Asci and S. Aydinyuz, Generalized k-order Fibonacci and Lucas hybrid numbers, Journal of Information and Optimization Sciences 42(8) (2021) 1765-1782. https://doi.org/10.1080/02522667.2021.1946238
  • [20] A. Szynal-Liana and I. Wloch, Introduction to Fibonacci and Lucas hybrinomials, Complex Variables and Elliptic Equations 65(10) (2020) 1736-1747.
  • [21] A. Szynal-Liana and I. Wloch, Generalized Fibonacci-Pell hybrinomials, Online Journal of Analytic Combinatorics 15 (2020), 1-12.
  • [22] M. O¨ zdemir, Introduction to hybrid numbers, Advances in Applied Clifford Algebras 28(11) (2018). https://doi.org/10.1007/s00006-018-0833-3
  • [23] C. Kızılates¸ and T. Kone, On special spacelike hybrid numbers with Fibonacci divisor number components, Indian Journal of Pure and Applied Mathematics (2022). https://doi.org/10.1007/s13226-022-00252-7
  • [24] A. Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae General Algebra and Applications 38 (2018) 91-98. doi: 10.7151/dmgaa. 1287
  • [25] N. Kilic, Introduction to k- Horadam hybrid numbers, Kuwait Journal of Science (2021). https://doi.org/10.48129/kjs.14929
  • [26] C. Kızılates¸, A note on Horadam hybrinomials, Fundamental Journal of Mathematics and Applications 5(1) (2022) 1-9. https://doi.org/10.33401/fujma.993546
  • [27] E. Sevgi, The generalized Lucas hybrinomials with two variables, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70(2) (2021) 622-630. https://doi.org/10.31801/cfsuasmas.854761
  • [28] D. Dumont, Matrices d’Euler-Seidel, Seminaire Lotharingien de Combinatorie 1981, B05c.
  • [29] R.L. Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics, Addison Wesley 1993.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Efruz Özlem Mersin

Mustafa Bahşi 0000-0002-6356-6592

Yayımlanma Tarihi 31 Ekim 2022
Gönderilme Tarihi 28 Haziran 2022
Kabul Tarihi 19 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 10 Sayı: 2

Kaynak Göster

APA Mersin, E. Ö., & Bahşi, M. (2022). Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp Journal of Mathematics, 10(2), 293-300.
AMA Mersin EÖ, Bahşi M. Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp J. Math. Ekim 2022;10(2):293-300.
Chicago Mersin, Efruz Özlem, ve Mustafa Bahşi. “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”. Konuralp Journal of Mathematics 10, sy. 2 (Ekim 2022): 293-300.
EndNote Mersin EÖ, Bahşi M (01 Ekim 2022) Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp Journal of Mathematics 10 2 293–300.
IEEE E. Ö. Mersin ve M. Bahşi, “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”, Konuralp J. Math., c. 10, sy. 2, ss. 293–300, 2022.
ISNAD Mersin, Efruz Özlem - Bahşi, Mustafa. “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”. Konuralp Journal of Mathematics 10/2 (Ekim 2022), 293-300.
JAMA Mersin EÖ, Bahşi M. Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp J. Math. 2022;10:293–300.
MLA Mersin, Efruz Özlem ve Mustafa Bahşi. “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”. Konuralp Journal of Mathematics, c. 10, sy. 2, 2022, ss. 293-00.
Vancouver Mersin EÖ, Bahşi M. Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp J. Math. 2022;10(2):293-300.
 Kapak Resmi İndir
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