Hyperbolic Horadam Functions

Hyperbolic Horadam Functions

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

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  • Stakhov, A. P., Rozin, B., “The "golden" hyperbolic models of Universe”, Chaos, Solitons & Fractals, 34(2): 159-171, (2007).
  • Falcón, S., Plaza, Á., “The k-Fibonacci hyperbolic functions”, Chaos, Solitons and Fractals, 38: 409- 420, (2008).
  • Horadam, A.F., “Basic properties of a certain generalized sequence of numbers”, The Fibonacci Quarterly, 3: 161-176, (1965).
  • Koçer, E.G., Tuğlu, N., Stakhov, A., “Hyperbolic Functions with Second Order Recurrence Sequences”, Ars Combinatoria, 88: 65-81, (2008).
  • De Spinadel, V.W., “From the Golden Mean to Chaos”, Nueva Libreria, (1998) (second edition, Nobuko, 2004).
  • 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, 77-6567: 1-32, (2006).
  • Stakhov, A. P., Tkachenko, I.S., “Hyperbolic Fibonacci trigonometry”, Reports of Ukraine Academy of Science, 7: 9-14 (1993).
  • Stakhov, A. P., Rozin, B., “On a new class of hyperbolic functions”, Chaos, Solitons & Fractals, 23(2): 379-389, (2005).
  • Stakhov, A. P., Rozin, B., “The Golden Shofar”, Chaos, Solitons & Fractals, 26(3): 677-684, (2005).
  • Stakhov, A. P., Rozin, B., “The continuous functions for the Fibonacci and Lucas p-numbers”, Chaos, Solitons & Fractals, 28(4): 1014-1025, (2006).
  • Vajda, S., “Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications”, Ellis Horwood Limited, (1989).
  • Baricza Á., Bhayo, B.A., Pogány, T.K., “Functional inequalities for generalized inverse trigonometric and hyperbolic functions”, Journal of Mathematical Analysis and Applications, 417: 244-259, (2014).
  • Cieśliński, J.L., “New definitions of exponential, hyperbolic and trigonometric functions on time scales”, Journal of Mathematical Analysis and Applications, 388: 8-22, (2012).
  • Klén, R., Vuorinen, M., Zhang, X.H., “Inequalities for the generalized trigonometric and hyperbolic functions”, Journal of Mathematical Analysis and Applications, 409: 521-529, (2014).
  • Lv, Y., Wang, G., Chu, Y., “A note on Jordan type inequalities for hyperbolic functions”, Applied Mathematics Letters, 25: 505-508, (2012).
  • Pandir, Y., Ulusoy, H., “New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations”, Journal of Mathematics, 2013: Article ID 201276, (2013).
  • Taşçı, D., Azman, H., “The k-Lucas Hyperbolic Functions”, Communications in Mathematics and Applications, 5(1): 11-21, (2014).
  • Yang, C.-Y., “Inequalities on generalized trigonometric and hyperbolic functions”, Journal of Mathematical Analysis and Applications, 419: 775-782, (2014).