SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2022 / Volume: 14 Issue: 2

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

Sure Köme(NEVŞEHİR HACI BEKTAŞ VELİ ÜNİVERSİTESİ)0000-0002-3558-0557
Pages
—
Publication Date
2022-12-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce the Wilker$-$Anglesio's inequality and parameterized Wilker inequality for the $k-$Fibonacci hyperbolic functions using classical analytical techniques.
📊
Key Findings & Data:In this paper, we introduce the Wilker$-$Anglesio's inequality and parameterized Wilker inequality for the $k-$Fibonacci hyperbolic functions using classical analytical techniques.
💡
Conclusion & Impact:In this paper, we introduce the Wilker$-$Anglesio's inequality and parameterized Wilker inequality for the $k-$Fibonacci hyperbolic functions using classical analytical techniques.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Wilker · Wilker-Anglesio inequality · parameterized Wilker-Anglesio inequality

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.

🔖

Cite This Article

Köme, S. (2022). Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science, Volume: 14 Issue: 2. https://doi.org/10.47000/tjmcs.974413

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. Bahşi, M., Wilker-type inequalities for hyperbolic Fibonacci functions, Journal of Inequalities and Applications, 1(2016), 1–7.
  2. Falcon, S., Plaza, A., On the Fibonacci k−numbers, Chaos, Solitons & Fractals, 32(5)(2007), 1615–1624.
  3. Falcon, S., Plaza, A., The k−Fibonacci sequence and the Pascal 2−triangle, Chaos, Solitons & Fractals, 33(1)(2007), 38–49.
  4. Falcon, S.,Plaza, A., The k−Fibonacci hyperbolic functions, Chaos, Solitons & Fractals, 38(2)(2008), 409–420.
  5. 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).
  6. Guo, B.N., Li, W., Qi, F., Proofs of Wilker’s inequalities involving trigonometric functions, Inequality Theory and Applications, 2(2003), 109–112.
  7. Hardy, G.H., Littlewood J.E., Polya, G., Inequalities, Cambridge University Press, 1952.
  8. Huygens C., Oeuvres Completes: Societe Hollandaise des Sciences, Den Haag, 1885.
  9. Kocer, E.G., Tuglu, N., Stakhov, A., Hyperbolic functions with second order recurrence sequences, Ars Combinatoria, 88(2008), 65–81.
  10. Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley & Sons, Washington, 2011.
  11. 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.
  12. Pinelis, I., L’Hospital rules for monotonicity and the Wilker-Anglesio inequality, The American Mathematical Monthly, 111(10)(2004), 905–909.
  13. Stakhov, A., Rozin, B., On a new class of hyperbolic functions, Chaos, Solitons & Fractals, 23(2)(2005), 379–389.
  14. Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio, J., Inequalities involving trigonometric functions, American Mathematical Monthly, 98(3)(1991), 264–267.
  15. Wilker, J.B., Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio,J., E3306, The American Mathematical Monthly., 98(3)(1991), 264–267.
  16. 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.
  17. Wu, S H., Debnath, L., Wilker-type inequalities for hyperbolic functions, Applied Mathematics Letters, 25(5)(2012), 837–842.
  18. Yazlık, Y., Köme, C., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25(4)(2018), 657–669.
  19. Zhang, L., Zhu, L., A new elementary proof of Wilker’s inequalities, Mathematical Inequalities and Applications, 11(1)(2008), 149.
  20. Zhu, L., A new simple proof of Wilker’s inequality, Mathematical Inequalities and Applications 8(4)(2005), 749.
  21. Zhu, L., On Wilker-type inequalities, Mathematical Inequalities and Applications, 10(4)(2007), 727.
  22. Zhu, L., Inequalities for hyperbolic functions and their applications, J. Inequal. Appl., 1(2010), 130821.