Successive Taylor Substitution and Automatic Proof of a Wilker-type Inequality with Parameter

Abstract

The problem of the maximum range of the parameter of Wilker-type inequality   2    3 3 ï¡ ï¡ ïƒ¦       sin x cos x x ＜ is successfully solved by machine proving with transcendental polynomial inequality proving programme Successive Taylor Substitution and artificial skills combined. Although the conclusions are known results, the method itself is exemplary for the same type of inequality.