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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).

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Mustafa BAHSI
AKSARAY ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ
0000-0002-6356-6592
Türkiye


Suleyman SOLAK
NECMETTİN ERBAKAN ÜNİVERSİTESİ, AHMET KELEŞOĞLU EĞİTİM FAKÜLTESİ
Türkiye

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

Cite

Bibtex @research article { gujs441422, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, address = {}, publisher = {Gazi University}, year = {2019}, volume = {32}, pages = {956 - 965}, doi = {10.35378/gujs.441422}, title = {Hyperbolic Horadam Functions}, key = {cite}, author = {Bahsı, Mustafa and Solak, Suleyman} }
APA Bahsı, M. & Solak, S. (2019). Hyperbolic Horadam Functions . Gazi University Journal of Science , 32 (3) , 956-965 . DOI: 10.35378/gujs.441422
MLA Bahsı, M. , Solak, S. "Hyperbolic Horadam Functions" . Gazi University Journal of Science 32 (2019 ): 956-965 <https://dergipark.org.tr/en/pub/gujs/issue/48219/441422>
Chicago Bahsı, M. , Solak, S. "Hyperbolic Horadam Functions". Gazi University Journal of Science 32 (2019 ): 956-965
RIS TY - JOUR T1 - Hyperbolic Horadam Functions AU - Mustafa Bahsı , Suleyman Solak Y1 - 2019 PY - 2019 N1 - doi: 10.35378/gujs.441422 DO - 10.35378/gujs.441422 T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 956 EP - 965 VL - 32 IS - 3 SN - -2147-1762 M3 - doi: 10.35378/gujs.441422 UR - https://doi.org/10.35378/gujs.441422 Y2 - 2019 ER -
EndNote %0 Gazi University Journal of Science Hyperbolic Horadam Functions %A Mustafa Bahsı , Suleyman Solak %T Hyperbolic Horadam Functions %D 2019 %J Gazi University Journal of Science %P -2147-1762 %V 32 %N 3 %R doi: 10.35378/gujs.441422 %U 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
AMA Bahsı M. , Solak S. Hyperbolic Horadam Functions. Gazi University Journal of Science. 2019; 32(3): 956-965.
Vancouver Bahsı M. , Solak S. Hyperbolic Horadam Functions. Gazi University Journal of Science. 2019; 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, Sep. 2019, doi:10.35378/gujs.441422