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

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.