# Questions tagged [karamata-inequality]

Inequalities, which we can prove by the Karamata's inequal;ity

4 questions
I'm interested by the following problem : Let $a,b,c,d$ be real positive numbers suc that $a\geq1$,$b\leq 1$ , $c\leq 1$ , $d\leq 1$ with conditions that I precise below then we have : $$a^{ab}+... 0answers 25 views ### General Method to solve Power Sum Inequality This is a general method to have power sum inequality . We work with x_i> 1 n real numbers . We want to show this kind of inequality : Let x_i> 1 be n real positive numbers and ... 0answers 69 views ### N-1 equal value principle Let us start with an example, consider the following sum:$$H_n=\sum_{i=1}^{n}\frac{1}{n-1+x_i} With $x_1x_2...x_n=1$, We're willing to show that $H_n \le 1$. To do this we start with the following ...
In fact it's my point of view but I think that this version of Niculescu's inequality is a mixture between Karamata and Jensen's inequality . So we have : Let $f(x)$ be a convex strictly ...