This paper presents a simple deduction of an inequality for heavy weighted triangles, and with it some new quadratic inequalities of three variants at any point within a triangle.
Finally, we provide an application of obtained result to the refinement of weighted power means inequality and weighted means inequality.
最后，我们应用所得结果给出加权幂平均不等式以及加权平均不等式的加细形式。
3
The two - parameters weighted mean in defined and an inequality for two - parameters weighted mean of convex function is prove, they have generalized and improved the results in literatures.