TY - JOUR T1 - Wilker-type Inequalities for $k-$Fibonacci Hyperbolic Functions AU - Köme, Sure PY - 2022 DA - December DO - 10.47000/tjmcs.974413 JF - Turkish Journal of Mathematics and Computer Science JO - TJMCS PB - Matematikçiler Derneği WT - DergiPark SN - 2148-1830 SP - 340 EP - 345 VL - 14 IS - 2 LA - en AB - In this paper, we introduce the Wilker$-$Anglesio's inequality and parameterized Wilker inequality for the $k-$Fibonacci hyperbolic functions using classical analytical techniques. KW - Wilker KW - Wilker-Anglesio inequality KW - parameterized Wilker-Anglesio inequality KW - $k-$Fibonacci hyperbolic functions CR - Bahşi, M., Wilker-type inequalities for hyperbolic Fibonacci functions, Journal of Inequalities and Applications, 1(2016), 1–7. CR - Falcon, S., Plaza, A., On the Fibonacci k−numbers, Chaos, Solitons & Fractals, 32(5)(2007), 1615–1624. CR - Falcon, S., Plaza, A., The k−Fibonacci sequence and the Pascal 2−triangle, Chaos, Solitons & Fractals, 33(1)(2007), 38–49. CR - Falcon, S.,Plaza, A., The k−Fibonacci hyperbolic functions, Chaos, Solitons & Fractals, 38(2)(2008), 409–420. CR - 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). CR - Guo, B.N., Li, W., Qi, F., Proofs of Wilker’s inequalities involving trigonometric functions, Inequality Theory and Applications, 2(2003), 109–112. CR - Hardy, G.H., Littlewood J.E., Polya, G., Inequalities, Cambridge University Press, 1952. CR - Huygens C., Oeuvres Completes: Societe Hollandaise des Sciences, Den Haag, 1885. CR - Kocer, E.G., Tuglu, N., Stakhov, A., Hyperbolic functions with second order recurrence sequences, Ars Combinatoria, 88(2008), 65–81. CR - Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley & Sons, Washington, 2011. CR - 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. CR - Pinelis, I., L’Hospital rules for monotonicity and the Wilker-Anglesio inequality, The American Mathematical Monthly, 111(10)(2004), 905–909. CR - Stakhov, A., Rozin, B., On a new class of hyperbolic functions, Chaos, Solitons & Fractals, 23(2)(2005), 379–389. CR - Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio, J., Inequalities involving trigonometric functions, American Mathematical Monthly, 98(3)(1991), 264–267. CR - Wilker, J.B., Sumner, J.S., Jagers, A.A., Vowe, M., Anglesio,J., E3306, The American Mathematical Monthly., 98(3)(1991), 264–267. CR - 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. CR - Wu, S H., Debnath, L., Wilker-type inequalities for hyperbolic functions, Applied Mathematics Letters, 25(5)(2012), 837–842. CR - Yazlık, Y., Köme, C., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25(4)(2018), 657–669. CR - Zhang, L., Zhu, L., A new elementary proof of Wilker’s inequalities, Mathematical Inequalities and Applications, 11(1)(2008), 149. CR - Zhu, L., A new simple proof of Wilker’s inequality, Mathematical Inequalities and Applications 8(4)(2005), 749. CR - Zhu, L., On Wilker-type inequalities, Mathematical Inequalities and Applications, 10(4)(2007), 727. CR - Zhu, L., Inequalities for hyperbolic functions and their applications, J. Inequal. Appl., 1(2010), 130821. UR - https://doi.org/10.47000/tjmcs.974413 L1 - https://dergipark.org.tr/en/download/article-file/1891763 ER -