Concise sharpening and generalizations of Shafer's inequality for the arc sine function

TL;DR

This paper presents a simplified method to sharpen and extend Shafer's inequality for the arc sine function, broadening its applicability and improving bounds.

Contribution

It introduces a concise, elementary approach to sharpen and generalize Shafer's inequality, extending known results in the field.

Findings

Sharpened bounds for the arc sine function.

Generalized Shafer's inequality.

Extended known inequalities.

Abstract

In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc sine function, and some known results are extended and generalized.