Sharp refined quadratic estimations of Shafer's inequalities

DOI10.3934/math.2021296zbMath1485.26018OpenAlexW3135861445MaRDI QIDQ2133245

Ling Zhu

Publication date: 29 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2021296

zbMATH Keywords

best constantslower bound for arctangentupper bound for arctangentShafer's inequalities

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Inequalities for sums, series and integrals (26D15) Inequalities for trigonometric functions and polynomials (26D05)

Cites Work

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• A refinement of the Becker-Stark inequalities
• A Berry-Esseen type bound for the kernel density estimator based on a weakly dependent and randomly left truncated data
• Sharpening of Jordan's type and Shafer-Fink's type inequalities with exponential approximations
• Padovan numbers as sums over partitions into odd parts
• Sharpening the Becker-Stark inequalities
• New inequalities of Shafer-Fink type for arc hyperbolic sine
• On Shafer-Fink-type inequality
• A method for proving some inequalities on mixed trigonometric polynomial functions
• On Shafer-Fink Inequalities
• On a quadratic estimate of Shafer
• A proof of an open problem of Yusuke Nishizawa for a power-exponential function
• Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
• On Quadratic Approximation

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