关于单调性和振荡性的Hopital型规则
On Hopital-style rules for monotonicity and oscillation
摘要：
我们指出了所谓的单调性和振荡性的Hôpital式规则与凹/凸函数的一些众所周知的性质的联系。从这个角度来看，我们能够推广的规则下没有可微性的要求，并大大扩展其可用性。改进的规则可以处理的情况下，其中涉及的函数具有非零的初始值，当导函数不一定是单调的。这种观点并不新鲜;它可以追溯到哈代，利特尔伍德和波利亚。
英文摘要：
We point out the connection of the so-called Hôpital-style rules for monotonicity and oscillation to some well-known properties of concave/convex functions. From this standpoint, we are able to generalize the rules under no differentiability requirements and greatly extend their usability. The improved rules can handle situations in which the functions involved have non-zero initial values and when the derived functions are not necessarily monotone. This perspective is not new; it can be dated back to Hardy, Littlewood and Polya.
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。
