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

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
\[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 – \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 0.\]

Keywords:

Trigonometric functions; Sin function; Inequalities.