Research Article
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Year 2022, , 340 - 345, 30.12.2022
https://doi.org/10.47000/tjmcs.974413

Abstract

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.

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

Year 2022, , 340 - 345, 30.12.2022
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.

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.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sure Köme 0000-0002-3558-0557

Publication Date December 30, 2022
Published in Issue Year 2022

Cite

APA 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.