涉及Seiffert等方法的几个尖锐不等式及其简明证明
Some sharp inequalities involving Seiffert and other means and their concise proofs
摘要：
本文通过建立涉及正弦函数和余弦函数的函数的单调性，给出了一些已知不等式的简洁证明，并找到了一些新的涉及两个正实数$a$和$b$的Seiffert、反调和、质心、算术、几何、调和和均方根均值的尖锐不等式，其中$a$和$b$具有$a\ne b$ .
英文摘要：
In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers $a$ and $b$ with $a\ne b$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
