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)


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.


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