Sharpening and generalizations of Shafer's inequality for the arc tangent function

TL;DR

This paper improves and extends Shafer's inequality for the arctangent function, refining existing results and providing more accurate bounds for the function.

Contribution

It introduces sharper and more general inequalities for the arctangent function, enhancing previous bounds and results.

Findings

Refined bounds for arctangent function

Generalized Shafer's inequality

Improved accuracy of existing inequalities

Abstract

In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.