New Inequalities for Hyperbolic Lucas Functions

Yıl 2022, Sayı: 41, 51 - 61, 31.12.2022

Ahmad Issa , Seyran İbrahimov

https://doi.org/10.53570/jnt.1162421

Cited By: 1

Öz

This article introduces the classic Wilker’s, Wu-Srivastava, Hugyen’s, Cusa-Hugyen’s, and Wilker’s-Anglesio type inequalities for hyperbolic Lucas functions with some new refinements.

Anahtar Kelimeler

Hyperbolic Lucas functions, Wilker’s inequality, Cusa-Huygens inequality, Wu-Srivastava inequality

Kaynakça

• B. N. Guo, B. M. Qiao, F. Qi, W. Li, On New Proofs of Wilker’s Inequalities Involving Trigonometric Functions, Mathematical Inequalities and Applications 6 (1) (2003) 19–22.
• B. N. Guo, W. Li, F. Qi, Proofs of Wilker’s Inequalities Involving Trigonometric Functions, Inequality Theory and Applications 2 (1) (2001) 109–112.
• E. Neuman, On Wilker and Huygens Type Inequalities, Mathematical Inequalities and Applications 15 (2) (2012) 271–279.
• E. Neuman, Wilker and Huygens-Type Inequalities for the Generalized Trigonometric and for the Generalized Hyperbolic Functions, Applied Mathematics and Computation 230 (2) (2014) 211–217.
• J. Wilker, J. Sumner, A. Jagers, M. Vowe, J. Anglesio, Inequalities Involving Trigonometric Functions (E3306), The American Mathematical Monthly 98 (3) (1991) 264–267.
• L. Zhang, L. Zhu, A New Elementary Proof of Wilker’s Inequalities, Mathematical Inequalities and Applications 11 (1) (2008) 149–151.
• L. Zhu, On Wilker-Type Inequalities, Mathematical Inequalities and Applications 10 (4) (2007) 727–731.
• M. Bahşi, Wilker-Type Inequalities for Hyperbolic Fibonacci Functions, Journal of Inequalities and Applications 2016 (1) (2016) 1–7.
• S. Wu, H. Srivastava, A Weighted and Exponential Generalization of Wilker’s Inequality and Its Applications, Integral Transforms and Special Functions 18 (8) (2007) 529–535.
• S.Wu, L. Debnath, Wilker-Type Inequalities for Hyperbolic Functions, Applied Mathematics Letters 25 (5) (2012) 837–842.
• W. D. Jiang, Q. M. Luo, F. Qi, Refinements and Sharpening of Some Huygens and Wilker Type Inequalities, Turkish Journal of Analysis and Number Theory 2 (4) (2014) 134–139.
• E. Neuman, J. Sandor, On Some Inequalities Involving Trigonometric and Hyperbolic Functions with Emphasis on the Cusa-Huygens, Wilker, and Huygens Inequalities, Mathematical Inequalities and Applications 13 (4) (2010) 715–723.
• C. Mortici, A Subtly Analysis of Wilker Inequality, Applied Mathematics and Computation 231 (15) (2014) 516–520.
• A. Baricz, J. Sandor, Extensions of the Generalized Wilker Inequality to Bessel Functions, Journal of Mathematical Inequalities 2 (3) (2008) 397–406.
• I. Pinelis, L’hospital Rules for Monotonicity and the Wilker-Anglesio Inequality, The American Mathematical Monthly 111 (10) (2004) 905–909.
• Y. J. Bagul, C. Chesneau, Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions, CUBO A Mathematical Journal 21 (1) (2019) 21–35.
• S. H. Wu, H. M. Srivastava, A further refinement of Wilker’s inequality, Integral Transforms and Special Functions 19 (10) (2008) 757–765.
• A. Stakhov, B. Rozin, On a New Class of Hyperbolic Functions, Chaos, Solitons & Fractals 23 (2) (2005) 379–389.
• A. Stakhov, On the General Theory of Hyperbolic Functions Based on the Hyperbolic Fibonacci and Lucas Functions and on Hilbert’s Fourth Problem, Mathematical Institute of the Serbian Academy of Sciences and Arts 15 (1) (2013) 1–16.
• K. Nantomah, Cusa-Huygens, Wilker and Huygens Type Inequalities for Generalized Hyperbolic Functions, Earthline Journal of Mathematical Sciences 5 (2) (2021) 277–289.
• K. Nantomah, E. Prempeh, Some Inequalities for Generalized Hyperbolic Functions, Moroccan Journal of Pure and Applied Analysis 6 (1) (2020) 76–92.
• D. S. Mitrinovic, J. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Springer, Dordrecht, 2013.
• G. Hardy, J. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1952.
• S. Ibrahimov, Inequalities Related to Generalized Hyperbolic Functions and Logarithmic Mean, Romanian Mathematical Magazine 2 (2022) 8 pages.