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Alternative proofs of Shafer's inequality for inverse hyperbolic tangent

Yogesh J. Bagul, Ramkrishna M. Dhaigude

Abstract

We point out that a concise proof of Theorem 2 in the article, 'On a quadratic estimate of Shafer' by L. Zhu contains a small mistake. Correcting this mistake and giving alternative proofs of Theorem 2 is the main aim of this note.

Alternative proofs of Shafer's inequality for inverse hyperbolic tangent

Abstract

We point out that a concise proof of Theorem 2 in the article, 'On a quadratic estimate of Shafer' by L. Zhu contains a small mistake. Correcting this mistake and giving alternative proofs of Theorem 2 is the main aim of this note.

Paper Structure

This paper contains 2 sections, 2 theorems, 25 equations.

Table of Contents

  1. Introduction and Correction
  2. Alternative simple proofs

Key Result

Theorem 1

Let $0 < x < \sqrt{15}/4.$ Then

Theorems & Definitions (2)

  • Theorem 1
  • Lemma 1