Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions

DOI10.1186/s13660-016-1157-2zbMath1346.26005OpenAlexW2510171489WikidataQ59466456 ScholiaQ59466456MaRDI QIDQ313559

Chao-Ping Chen, Jun-ling Sun

Publication date: 12 September 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-1157-2

zbMATH Keywords

inequalitiesinverse trigonometric functionslemniscate function

Mathematics Subject Classification ID

Inequalities involving other types of functions (26D07)

Related Items (10)

Approximations to inverse tangent function ⋮ A method to prove inequalities and its applications ⋮ Padé approximant related to inequalities for Gauss lemniscate functions ⋮ Inequalities related to certain inverse trigonometric and inverse hyperbolic functions ⋮ Refined estimates and generalizations of inequalities related to the arctangent function and Shafer's inequality ⋮ A constructive method for approximating trigonometric functions and their integrals ⋮ Refined quadratic estimations of Shafer's inequality ⋮ Monotonicity and inequalities related to the generalized inverse lemniscate functions ⋮ Several Optimal Bounds for Some Means Derived from the Lemniscatic Mean ⋮ The monotonicity of ratios involving arc tangent function with applications

Cites Work

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• Estimates for the arctangent function related to Shafer's inequality
• On a quadratic estimate of Shafer
• Wilker and Huygens type inequalities for the Lemniscate functions
• Wilker and Huygens type inequalities for the Lemniscate functions, II
• On lemniscate functions
• Algorithms Involving Arithmetic and Geometric Means
• On Quadratic Approximation

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