Inequalities related to certain inverse trigonometric and inverse hyperbolic functions

DOI10.1007/s13398-020-00836-0zbMath1436.26013OpenAlexW3012344327MaRDI QIDQ2173665

Yanyan Li

Publication date: 17 April 2020

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-020-00836-0

zbMATH Keywords

inequalitiesinverse hyperbolic tangent functioninverse sine functioninverse hyperbolic sine functioninverse tangent function

Mathematics Subject Classification ID

Inequalities for trigonometric functions and polynomials (26D05) Computational methods for problems pertaining to real functions (26-08)

Related Items (9)

A method to prove inequalities and its applications ⋮ A generic inequality for basic special functions ⋮ New double inequality of Masjed-Jamei-type ⋮ New inequalities for hyperbolic functions based on reparameterization ⋮ Monotonous two-parameter functions for asymptoticly approximating the inequalities involving the inverse tangent functions ⋮ Tighter bounds for the inequalities of sinc function based on reparameterization ⋮ New bounds of Wilker- and Huygens-type inequalities for inverse trigonometric functions ⋮ Sharp inequalities on circular and hyperbolic functions using Bernoulli inequality types ⋮ New inequalities between the inverse hyperbolic tangent and the analogue for corresponding functions

Uses Software

• Maple
• DLMF

Cites Work

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• Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions
• A main inequality for several special functions
• Some generalizations of the Cauchy-Schwarz and the Cauchy-Bunyakovsky inequalities involving four free parameters and their applications
• Approximations to inverse tangent function
• Inequalities between the inverse hyperbolic tangent and the inverse sine and the analogue for corresponding functions
• A method for proving some inequalities on mixed trigonometric polynomial functions
• On a quadratic estimate of Shafer

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