The relationship between Huygens’ and Wilker’s inequalities and further remarks

DOI10.2298/aadm210727012czbMath1524.26026OpenAlexW4366522948MaRDI QIDQ6169404

Chao-Ping Chen, Cristinel Mortici

Publication date: 11 July 2023

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/aadm210727012c

zbMATH Keywords

inequalitiesWilker inequalityHuygens inequalityCusa inequality

Mathematics Subject Classification ID

Inequalities for trigonometric functions and polynomials (26D05)

Cites Work

• Sharp Cusa and Becker-Stark inequalities
• Wilker-type inequalities for hyperbolic functions
• The proof of Muqattash-Yahdi conjecture
• A source of inequalities for circular functions
• Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions
• A subtly analysis of Wilker inequality
• Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities
• New approximations of some expressions involving trigonometric functions
• The natural algorithmic approach of mixed trigonometric-polynomial problems
• New inequalities of Wilker's type for hyperbolic functions
• Some notes on a method for proving inequalities by computer
• On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
• A New Simple Proof of Wilker's Inequality
• Extensions of the generalized Wilker inequality to Bessel functions
• Wilker and Huygens type inequalities for the Lemniscate functions
• The natural approach of Wilker-Cusa-Huygens inequalities
• A new elementary proof of Wilker's inequalities
• A weighted and exponential generalization of Wilker's inequality and its applications

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