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April 10, 2026Applicable Analysis and Discrete Mathematics0 citationsOpen Access

New Shafer-Fink type inequalities for inverse trigonometric, inverse hyperbolic and arc lemniscate functions

SXShuai XuJSJunling SunCCChao-Ping Chen

Key Points

  • The aim is to establish new Shafer-Fink type inequalities for various inverse functions.
  • Developed inequalities for the arc sine and arc tangent functions.
  • Created sharp two-sided inequalities for the arc hyperbolic tangent function.
  • Established a new lower bound for the arc hyperbolic tangent function.
  • Introduced new sharp inequalities for arc lemniscate functions.
  • Presented new inequalities that provide tighter bounds for the arc sine and arc tangent functions.
  • Achieved sharp two-sided inequalities for the arc hyperbolic tangent function.
  • Introduced a novel lower bound, enhancing understanding of the arc hyperbolic tangent function.

Abstract

In this paper, we present new Shafer-Fink type inequalities for the arc sine and arc tangent functions. We develop Shafer?s inequality for the arc hyperbolic tangent function to produce sharp two-sided inequalities, and present a new lower bound for the arc hyperbolic tangent function. Also, we present new sharp inequalities for the arc lemniscate functions.

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Cite This Study

Xu et al. (2026) studied this question.

synapsesocial.com/papers/69d893eb6c1944d70ce04e20https://doi.org/10.2298/aadm250324010x
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