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math.GM2021★ 2 cited
Alternative proofs of Shafer's inequality for inverse hyperbolic tangent
Yogesh J. Bagul, Ramkrishna M. Dhaigude
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 alternativ…
math.GM2020
Wilker and Huygens type inequalities for mixed trigonometric-hyperbolic functions
Yogesh J. Bagul, Ramkrishna M. Dhaigude, Barkat A. Bhayo +1
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,…