arXiv subjects

Ramkrishna M. Dhaigude

Publications and source records attributed to Ramkrishna M. Dhaigude.

2 recordsLinked to original sources

arXiv2022

Alternative proofs of Shafer's inequality for inverse hyperbolic tangent

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.

math.GM↗

arXiv2020

Wilker and Huygens type inequalities for mixed trigonometric-hyperbolic functions

Motivated by the work of J. Sándor [19], in this paper we establish a new Wilker type and Huygens type inequalities involving the trigonometric and hyperbolic functions. Moreover, in terms of hyperbolic functions, the upper and lower bounds of sin(x)/x and tan(x)/x are given.

math.GM↗