一类迭代方程可微解的讨论

A Kind of Iterative Equation Differentiable Solution Discussion

在数学领域,迭代理论的应用非常广泛。针对一类迭代方程当中,是否存在可微性解的问题进行探讨,以期得到对于一类迭代方程而言,可微解存在与否的相应条件。首先对一类迭代方程当中的基本的概念以及引理进行了说明,而后结合不动点以及相应函数映射的概念,得到了三个与不动点数量相关的判定定理,同时对判定定理进行求证并进一步进行数学实例的说明。经过实际求证并结合数学图形,表明对于函数g,其不动点存在的三种情况下,对应的f f=g均不存在相应的可微性解。

In the field of mathematics,iteration theory has a wide range of applications.In order to discuss whether there is a differentiability connection in a class of iterative equations,in order to obtain the corresponding conditions for the existence or absence of differentiable solutions for a class of iterative equations.The discussion begins with the explanation of the basic concepts and lemma in a class of iterative equations.Then,combined with the concepts of fixed points and corresponding function mappings,three decision theorems related to the number of fixed points are obtained,and the decision theorems are verified and mathematical examples are further explained.After actual verification and combined with mathematical graphics,it is shown that for the function g,there is no corresponding differentiable solution in the three cases where its fixed point exists,and the corresponding f f=g does not exist.