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Hyperbolic Horadam Functions

Year 2019, Volume: 32 Issue: 3, 956 - 965, 01.09.2019
https://doi.org/10.35378/gujs.441422

Abstract

This article introduce hyperbolic functions connected to Horadam sequence. That is, we define hyperbolic Horadam functions and present their hyperbolic and recursive properties. We give some geometrical properties of hyperbolic Horadam functions.

References

  • [1] Baricza Á., Bhayo, B.A. and Pogány, T.K., “Functional inequalities for generalized inverse trigonometric and hyperbolic functions”, J. Math. Anal. Appl. 417, 244-259, (2014).
  • [2] Cieśliński, J.L., “New definitions of exponential, hyperbolic and trigonometric functions on time scales”, J. Math. Anal. Appl. 388, 8-22, (2012).
  • [3] Falcón, S. and Plaza, Á., “The k-Fibonacci hyperbolic functions”, Chaos, Solitons and Fractals, 38, 409-420, (2008).
  • [4] Horadam, A.F., “Basic properties of a certain generalized sequence of numbers”, The Fibonacci Quart. 3, 161-176, (1965).
  • [5] Klén, R., Vuorinen, M. and Zhang, X.H., “Inequalities for the generalized trigonometric and hyperbolic functions”, J. Math. Anal. Appl. 409, 521-529, (2014).
  • [6] Koçer, E.G., Tuğlu, N. and Stakhov, A., “Hyperbolic Functions with Second Order Recurrence Sequences”, Ars Combinatoria, 88, 65-81, (2008).
  • [7] Lv, Y., Wang, G. and Chu, Y., “A note on Jordan type inequalities for hyperbolic functions”, Applied Mathematics Letters, 25, 505-508, (2012).
  • [8] Pandir, Y. and Ulusoy, H., “New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations”, Journal of Mathematics Volume 2013, Article ID 201276, (2013).
  • [9] De Spinadel, V.W., “From the Golden Mean to Chaos”, Nueva Libreria, 1998 (second edition, Nobuko, 2004).
  • [10] Stakhov, A. P., “Gazale Formulas, a New Class of the Hyperbolic Fibonacci and Lucas Functions, and the Improved Method of the `Golden' Cryptography”, Academy of Trinitarism, No. 77-6567, 1-32, 2006.
  • [11] Stakhov, A. P. and Tkachenko, I.S., “Hyperbolic Fibonacci trigonometry”, Rep Ukr. Acad. Sci. 7, 9-14 (1993).
  • [12] Stakhov, A. P. and Rozin, B., “On a new class of hyperbolic functions”, Chaos, Solitons & Fractals, 23:(2), 379-389, (2005).
  • [13] Stakhov, A. P. and Rozin, B., “The Golden Shofar”, Chaos, Solitons & Fractals, 26:(3), 677-684, (2005).
  • [14] Stakhov, A. P. and Rozin, B., “The continuous functions for the Fibonacci and Lucas p-numbers”, Chaos, Solitons & Fractals, 28:(4), 1014-1025, (2006).
  • [15] Stakhov, A. P. and Rozin, B., “The "golden" hyperbolic models of Universe”, Chaos, Solitons & Fractals, 34:(2), 159-171, (2007).
  • [16] Taşçı, D. and Azman, H., “The k-Lucas Hyperbolic Functions, Communications in Mathematics and Applications”, 5:(1), 11-21, (2014).
  • [17] Vajda, S., “Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications”, Ellis Horwood Limited. 1989.
  • [18] Yang, C.-Y., “Inequalities on generalized trigonometric and hyperbolic functions”, J. Math. Anal. Appl. 419, 775-782, (2014).
Year 2019, Volume: 32 Issue: 3, 956 - 965, 01.09.2019
https://doi.org/10.35378/gujs.441422

Abstract

References

  • [1] Baricza Á., Bhayo, B.A. and Pogány, T.K., “Functional inequalities for generalized inverse trigonometric and hyperbolic functions”, J. Math. Anal. Appl. 417, 244-259, (2014).
  • [2] Cieśliński, J.L., “New definitions of exponential, hyperbolic and trigonometric functions on time scales”, J. Math. Anal. Appl. 388, 8-22, (2012).
  • [3] Falcón, S. and Plaza, Á., “The k-Fibonacci hyperbolic functions”, Chaos, Solitons and Fractals, 38, 409-420, (2008).
  • [4] Horadam, A.F., “Basic properties of a certain generalized sequence of numbers”, The Fibonacci Quart. 3, 161-176, (1965).
  • [5] Klén, R., Vuorinen, M. and Zhang, X.H., “Inequalities for the generalized trigonometric and hyperbolic functions”, J. Math. Anal. Appl. 409, 521-529, (2014).
  • [6] Koçer, E.G., Tuğlu, N. and Stakhov, A., “Hyperbolic Functions with Second Order Recurrence Sequences”, Ars Combinatoria, 88, 65-81, (2008).
  • [7] Lv, Y., Wang, G. and Chu, Y., “A note on Jordan type inequalities for hyperbolic functions”, Applied Mathematics Letters, 25, 505-508, (2012).
  • [8] Pandir, Y. and Ulusoy, H., “New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations”, Journal of Mathematics Volume 2013, Article ID 201276, (2013).
  • [9] De Spinadel, V.W., “From the Golden Mean to Chaos”, Nueva Libreria, 1998 (second edition, Nobuko, 2004).
  • [10] Stakhov, A. P., “Gazale Formulas, a New Class of the Hyperbolic Fibonacci and Lucas Functions, and the Improved Method of the `Golden' Cryptography”, Academy of Trinitarism, No. 77-6567, 1-32, 2006.
  • [11] Stakhov, A. P. and Tkachenko, I.S., “Hyperbolic Fibonacci trigonometry”, Rep Ukr. Acad. Sci. 7, 9-14 (1993).
  • [12] Stakhov, A. P. and Rozin, B., “On a new class of hyperbolic functions”, Chaos, Solitons & Fractals, 23:(2), 379-389, (2005).
  • [13] Stakhov, A. P. and Rozin, B., “The Golden Shofar”, Chaos, Solitons & Fractals, 26:(3), 677-684, (2005).
  • [14] Stakhov, A. P. and Rozin, B., “The continuous functions for the Fibonacci and Lucas p-numbers”, Chaos, Solitons & Fractals, 28:(4), 1014-1025, (2006).
  • [15] Stakhov, A. P. and Rozin, B., “The "golden" hyperbolic models of Universe”, Chaos, Solitons & Fractals, 34:(2), 159-171, (2007).
  • [16] Taşçı, D. and Azman, H., “The k-Lucas Hyperbolic Functions, Communications in Mathematics and Applications”, 5:(1), 11-21, (2014).
  • [17] Vajda, S., “Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications”, Ellis Horwood Limited. 1989.
  • [18] Yang, C.-Y., “Inequalities on generalized trigonometric and hyperbolic functions”, J. Math. Anal. Appl. 419, 775-782, (2014).
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Mustafa Bahsı

Suleyman Solak

Publication Date September 1, 2019
Published in Issue Year 2019 Volume: 32 Issue: 3

Cite

APA Bahsı, M., & Solak, S. (2019). Hyperbolic Horadam Functions. Gazi University Journal of Science, 32(3), 956-965. https://doi.org/10.35378/gujs.441422
AMA Bahsı M, Solak S. Hyperbolic Horadam Functions. Gazi University Journal of Science. September 2019;32(3):956-965. doi:10.35378/gujs.441422
Chicago Bahsı, Mustafa, and Suleyman Solak. “Hyperbolic Horadam Functions”. Gazi University Journal of Science 32, no. 3 (September 2019): 956-65. https://doi.org/10.35378/gujs.441422.
EndNote Bahsı M, Solak S (September 1, 2019) Hyperbolic Horadam Functions. Gazi University Journal of Science 32 3 956–965.
IEEE M. Bahsı and S. Solak, “Hyperbolic Horadam Functions”, Gazi University Journal of Science, vol. 32, no. 3, pp. 956–965, 2019, doi: 10.35378/gujs.441422.
ISNAD Bahsı, Mustafa - Solak, Suleyman. “Hyperbolic Horadam Functions”. Gazi University Journal of Science 32/3 (September 2019), 956-965. https://doi.org/10.35378/gujs.441422.
JAMA Bahsı M, Solak S. Hyperbolic Horadam Functions. Gazi University Journal of Science. 2019;32:956–965.
MLA Bahsı, Mustafa and Suleyman Solak. “Hyperbolic Horadam Functions”. Gazi University Journal of Science, vol. 32, no. 3, 2019, pp. 956-65, doi:10.35378/gujs.441422.
Vancouver Bahsı M, Solak S. Hyperbolic Horadam Functions. Gazi University Journal of Science. 2019;32(3):956-65.

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