涉及Cater循环函数的循环不等式
Cyclic inequalities involving Cater cyclic function
摘要：
利用数学分析理论、不等式理论、数学归纳法和降维方法，在适当的假设下，建立了如下循环不等式：\[\sum_{i=1}^{n} {a_i^{a_{n+1-i}}}\leq\sum_{\text{cyc}:~n}^{1\leq i\leq n} {a_i^{a_{i + 1}}}\leq \sum_{i=1}^{n} {a_i^{a_i}},~\forall n\geq2.\]
英文摘要：
By means of the mathematical analysis theory, inequality theory, mathematical induction and the dimension reduction method, under the proper hypotheses, we establish the following cyclic inequalities: \[\sum_{i=1}^{n} {a_i^{a_{n+1-i}}}\leq\sum_{\text{cyc}:~n}^{1\leq i\leq n} {a_i^{a_{i + 1}}}\leq \sum_{i=1}^{n} {a_i^{a_i}},~\forall n\geq2.\]
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。
