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We determine the best positive constants a and b such that
Similar sharp inequalities are also considered.
- Trigonometric functions
- Hyperbolic functions
- Monotonicity theorems
- Hardy, G.H., J.E. Littlewood, G. Pólya. Inequalities, Cambridge Univ. Press, 1959.
- Neuman, E., J. Sándor, On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa–Huygens, Wilker, and Huygens inequalities, Math. Ineq. Appl., Vol. 13, 2010, No. 4, 715–723.
- Neuman, E., J. Sándor, Optimal inequalities for hyperbolic and trigonometric functions, Bull. Math. Anal. Appl., Vol. 3, 2011, No. 3, 177–181.
- Sándor, J., Two sharp inequalities for trigonometric and hyperbolic functions, ath. Ineq. Appl., to appear
Cite this paperAPA
Sándor, J. (2013). Sharp Cusa–Huygens and related inequalities, Notes on Number Theory and Discrete Mathematics, 19(1), 50-54.Chicago
Sándor, József. “Sharp Cusa–Huygens and related inequalities.” Notes on Number Theory and Discrete Mathematics 19, no. 1 (2013): 50-54.MLA
Sándor, József. “Sharp Cusa–Huygens and related inequalities.” Notes on Number Theory and Discrete Mathematics 19.1 (2013): 50-54. Print.