Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions

Year 2022, Volume: 14 Issue: 2, 340 - 345, 30.12.2022

Sure Köme

https://doi.org/10.47000/tjmcs.974413

Abstract

In this paper, we introduce the Wilker$-$Anglesio's inequality and parameterized Wilker inequality for the $k-$Fibonacci hyperbolic functions using classical analytical techniques.

Keywords

Wilker , Wilker-Anglesio inequality , parameterized Wilker-Anglesio inequality , $k-$Fibonacci hyperbolic functions

References

• Bahşi, M., Wilker-type inequalities for hyperbolic Fibonacci functions, Journal of Inequalities and Applications, 1(2016), 1–7.
• Falcon, S., Plaza, A., On the Fibonacci k−numbers, Chaos, Solitons & Fractals, 32(5)(2007), 1615–1624.
• Falcon, S., Plaza, A., The k−Fibonacci sequence and the Pascal 2−triangle, Chaos, Solitons & Fractals, 33(1)(2007), 38–49.
• Falcon, S.,Plaza, A., The k−Fibonacci hyperbolic functions, Chaos, Solitons & Fractals, 38(2)(2008), 409–420.
• Guo, B.N., Li, W., Qiao, B.M., Qi, F., On new proofs of inequalities involving trigonometric functions, RGMIA Research Report Collection, 3(1)(2000).
• Guo, B.N., Li, W., Qi, F., Proofs of Wilker’s inequalities involving trigonometric functions, Inequality Theory and Applications, 2(2003), 109–112.
• Hardy, G.H., Littlewood J.E., Polya, G., Inequalities, Cambridge University Press, 1952.
• 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.