# Shafer-Fink type inequalities for arc lemniscate functions

## TL;DR

This paper establishes sharp Shafer-Fink type inequalities for arc lemniscate and hyperbolic arc lemniscate functions, enhancing understanding of their monotonicity and bounds.

## Contribution

It introduces new sharp inequalities for arc lemniscate functions, extending Shafer-Fink inequalities to these special functions.

## Key findings

- Proved sharp Shafer-Fink type inequalities for arc lemniscate functions.
- Analyzed monotonicity properties of functions involving arc lemniscate.
- Extended inequalities to hyperbolic arc lemniscate functions.

## Abstract

In this paper, we investigate the monotonicity and inequalities for some functions involving the arc lemniscate and the hyperbolic arc lemniscate functions. In particular, sharp Shafer-Fink type inequalities for the arc lemniscate and the hyperbolic arc lemniscate functions are proved.