Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 19 – 34
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0196
Sharp inequalities related to Wilker results
Abd Raouf Chouikha
4, Cour des Quesblais 35430 Saint-Pere, France; chouikha@math.univ-paris13.fr
Copyright © 2023 Abd Raouf Chouikha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: October 20, 2022 – Accepted: March 1, 2023 – Published: March 31, 2023
Abstract
In this paper, we interested in Wilker inequalities. We provide finer bounds than known previous. Moreover, bounds are obtained for the following trigonometric function
\[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 – \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 0.\]
\[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 – \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 0.\]
Keywords:
Trigonometric functions; Sin function; Inequalities.