Huygens C., Oeuvres Completes: Societe Hollandaise des Sciences, Den Haag, 1885.
Kocer, E.G., Tuglu, N., Stakhov, A., Hyperbolic functions with second order recurrence sequences, Ars Combinatoria, 88(2008), 65–81.
Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley & Sons, Washington, 2011.
Neuman, E., Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions, Applied Mathematics and Computation, 230(2014), 211–217.
Pinelis, I., L’Hospital rules for monotonicity and the Wilker-Anglesio inequality, The American Mathematical Monthly, 111(10)(2004), 905–909.
Stakhov, A., Rozin, B., On a new class of hyperbolic functions, Chaos, Solitons & Fractals, 23(2)(2005), 379–389.
Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio, J., Inequalities involving trigonometric functions, American Mathematical Monthly, 98(3)(1991), 264–267.
Wilker, J.B., Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio,J., E3306, The American Mathematical Monthly., 98(3)(1991), 264–267.
Wu, S.H., Srivastava, H.M, A weighted and exponential generalization of Wilker’s inequality and its applications, Integral Transforms and Special Functions, 18(8)(2007), 529–535.
Wu, S H., Debnath, L., Wilker-type inequalities for hyperbolic functions, Applied Mathematics Letters, 25(5)(2012), 837–842.
Yazlık, Y., Köme, C., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25(4)(2018), 657–669.
Zhang, L., Zhu, L., A new elementary proof of Wilker’s inequalities, Mathematical Inequalities and Applications, 11(1)(2008), 149.
Zhu, L., A new simple proof of Wilker’s inequality, Mathematical Inequalities and Applications 8(4)(2005), 749.
Zhu, L., On Wilker-type inequalities, Mathematical Inequalities and Applications, 10(4)(2007), 727.
Zhu, L., Inequalities for hyperbolic functions and their applications, J. Inequal. Appl., 1(2010), 130821.
Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions
In this paper, we introduce the Wilker$-$Anglesio's inequality and parameterized Wilker inequality for the $k-$Fibonacci hyperbolic functions using classical analytical techniques.
Huygens C., Oeuvres Completes: Societe Hollandaise des Sciences, Den Haag, 1885.
Kocer, E.G., Tuglu, N., Stakhov, A., Hyperbolic functions with second order recurrence sequences, Ars Combinatoria, 88(2008), 65–81.
Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley & Sons, Washington, 2011.
Neuman, E., Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions, Applied Mathematics and Computation, 230(2014), 211–217.
Pinelis, I., L’Hospital rules for monotonicity and the Wilker-Anglesio inequality, The American Mathematical Monthly, 111(10)(2004), 905–909.
Stakhov, A., Rozin, B., On a new class of hyperbolic functions, Chaos, Solitons & Fractals, 23(2)(2005), 379–389.
Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio, J., Inequalities involving trigonometric functions, American Mathematical Monthly, 98(3)(1991), 264–267.
Wilker, J.B., Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio,J., E3306, The American Mathematical Monthly., 98(3)(1991), 264–267.
Wu, S.H., Srivastava, H.M, A weighted and exponential generalization of Wilker’s inequality and its applications, Integral Transforms and Special Functions, 18(8)(2007), 529–535.
Wu, S H., Debnath, L., Wilker-type inequalities for hyperbolic functions, Applied Mathematics Letters, 25(5)(2012), 837–842.
Yazlık, Y., Köme, C., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25(4)(2018), 657–669.
Zhang, L., Zhu, L., A new elementary proof of Wilker’s inequalities, Mathematical Inequalities and Applications, 11(1)(2008), 149.
Zhu, L., A new simple proof of Wilker’s inequality, Mathematical Inequalities and Applications 8(4)(2005), 749.
Zhu, L., On Wilker-type inequalities, Mathematical Inequalities and Applications, 10(4)(2007), 727.
Zhu, L., Inequalities for hyperbolic functions and their applications, J. Inequal. Appl., 1(2010), 130821.
Köme, S. (2022). Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science, 14(2), 340-345. https://doi.org/10.47000/tjmcs.974413
AMA
Köme S. Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions. TJMCS. December 2022;14(2):340-345. doi:10.47000/tjmcs.974413
Chicago
Köme, Sure. “Wilker-Type Inequalities for $k-$Fibonacci Hyperbolic Functions”. Turkish Journal of Mathematics and Computer Science 14, no. 2 (December 2022): 340-45. https://doi.org/10.47000/tjmcs.974413.
EndNote
Köme S (December 1, 2022) Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science 14 2 340–345.
IEEE
S. Köme, “Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions”, TJMCS, vol. 14, no. 2, pp. 340–345, 2022, doi: 10.47000/tjmcs.974413.
ISNAD
Köme, Sure. “Wilker-Type Inequalities for $k-$Fibonacci Hyperbolic Functions”. Turkish Journal of Mathematics and Computer Science 14/2 (December 2022), 340-345. https://doi.org/10.47000/tjmcs.974413.
JAMA
Köme S. Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions. TJMCS. 2022;14:340–345.
MLA
Köme, Sure. “Wilker-Type Inequalities for $k-$Fibonacci Hyperbolic Functions”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 2, 2022, pp. 340-5, doi:10.47000/tjmcs.974413.
Vancouver
Köme S. Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions. TJMCS. 2022;14(2):340-5.