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Combine my first previous question and second previous question with the Muirhead inequality. I have posed conjectures of two inequalities as follows: Inequality 1: Let $n>2$ and $1 \le m \le n$...

I improve my previous question. Because this conjecture is exactly natural development of A Muirhead Like Inequality and Muirhead's Inequality so I think the conjecture is true. But I can not prove it....