Jñānābha, Vol. 51 (1) (2021), (101-108)
ON SIMPLE BOUNDS FOR INVERSE HYPERBOLIC SINE AND INVERSE HYPERBOLIC TANGENT FUNCTIONS
By
Ramkrishna M. Dhaigude, Sumedh B. Thool
Department of Mathematics, Government Vidarbha Institute of Science and Humanities, Amravati-444604, Maharashtra, India Email:rmdhaigude@gmail.com, sumedhmaths@gmail.com
Yogesh J. Bagul
Department of Mathematics, K. K. M. College, Manwath, Dist: Parbhani-431505, Maharashtra, India
Email:yjbagul@gmail.com
and
Vinay M. Raut
Department of Mathematics, Shri. Shivaji Science College Amravati-444603, Maharashtra, India
Email:vinayraut18@gmail.com
(Received : April 04, 2021 ; Revised : April 22, 2021)
DOI: https://doi.org/10.58250/Jnanabha.2021.51114
Abstract
We obtain simple algebraic bounds of inverse hyperbolic sine and inverse hyperbolic tangent functions i.e., sinh⁻¹ x and tanh⁻¹ x. The inequalities are obtained on the entire domains of these functions. From our results, we obtain tighter bounds for the same functions. The Wilker and Huygens type inequalities involving inverse hyperbolic functions can also be easily derived from our main results.
2010 Mathematics Subject Classifications: 26D07, 26D20, 42A10
Keywords and phrases: Inverse hyperbolic sine function, inverse hyperbolic tangent function, Wilker and Huygens type inequalities, increasing-decreasing functions.