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Hyper-Fibonacci and Hyper-Lucas Hybrinomials

Year 2022, Volume: 10 Issue: 2, 293 - 300, 31.10.2022

Efruz Özlem Mersin Mustafa Bahşi

Abstract

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.

Keywords

Hybrinomials Hyper-Fibonacci numbers Hyper-Lucas numbers Polynomials

References

  • [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.

Year 2022, Volume: 10 Issue: 2, 293 - 300, 31.10.2022

Efruz Özlem Mersin Mustafa Bahşi

Abstract

References

  • [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.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Efruz Özlem Mersin

Mustafa Bahşi 0000-0002-6356-6592

Publication Date October 31, 2022
Submission Date June 28, 2022
Acceptance Date September 19, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

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. October 2022;10(2):293-300.
Chicago Mersin, Efruz Özlem, and Mustafa Bahşi. “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 293-300.
EndNote Mersin EÖ, Bahşi M (October 1, 2022) Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp Journal of Mathematics 10 2 293–300.
IEEE E. Ö. Mersin and M. Bahşi, “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”, Konuralp J. Math., vol. 10, no. 2, pp. 293–300, 2022.
ISNAD Mersin, Efruz Özlem - Bahşi, Mustafa. “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”. Konuralp Journal of Mathematics 10/2 (October 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 and Mustafa Bahşi. “Hyper-Fibonacci and Hyper-Lucas Hybrinomials”. Konuralp Journal of Mathematics, vol. 10, no. 2, 2022, pp. 293-00.
Vancouver Mersin EÖ, Bahşi M. Hyper-Fibonacci and Hyper-Lucas Hybrinomials. Konuralp J. Math. 2022;10(2):293-300.
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