Necessary and sufficient conditions for the two parameter generalized Wilker-type inequalities
Necessary and sufficient conditions for the two parameter generalized Wilker-type inequalities
In the article, we provide the necessary and sufficient conditions for the parameters α and β such that the generalized Wilker-type inequality $$ \frac{2\beta}{\alpha+2\beta} \biggl(\frac{\sin x}{x} \biggr)^{\alpha}+ \frac{\alpha}{\alpha+2\beta} \biggl(\frac{\tan x}{x} \biggr)^{\beta}-1>(< )0 $$ holds for all $x\in(0, \pi/2)$ .