Some new inequalities of the Huygens type

DOI10.1016/j.camwa.2009.07.045zbMath1189.26030OpenAlexW2077247485MaRDI QIDQ979935

Ling Zhu

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.07.045

zbMATH Keywords

hyperbolic functionscircular functionsHuygens type inequalitiesthe reciprocals of circular functionsthe reciprocals of hyperbolic functions

Mathematics Subject Classification ID

Inequalities for trigonometric functions and polynomials (26D05)

Related Items (14)

Extension of Huygens type inequalities for Bessel and modified Bessel Functions ⋮ Topics in Special Functions III ⋮ Sharpness of Wilker and Huygens type inequalities ⋮ Sharp Wilker-type inequalities with applications ⋮ Inequalities for hyperbolic functions and their applications ⋮ On Jordan type inequalities for hyperbolic functions ⋮ Unnamed Item ⋮ Lazarević and Cusa type inequalities for hyperbolic functions with two parameters and their applications ⋮ New Wilker-type and Huygens-type inequalities ⋮ Some new results of Mitrinović-Cusa's and related inequalities based on the interpolation and approximation method ⋮ Sharp inequalities of Mitrinovic-Adamovic type ⋮ Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities. II ⋮ An unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities and the analogue for hyperbolic functions ⋮ Sharp Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions

Cites Work

• Unnamed Item
• Unnamed Item
• A general refinement of Jordan-type inequality
• Generalized elliptic integrals and modular equations
• Inequalities for quasiconformal mappings in space
• Sharpening Jordan's inequality and Yang Le inequality. II
• A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality
• Sharpening Jordan's inequality and the Yang Le inequality
• A general refinement of Jordan's inequality and a refinement of L. Yang's inequality
• A weighted and exponential generalization of Wilker's inequality and its applications
• Sharpening of Jordan's inequalities and its applications

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