We consider continuous mappings between two Banach spaces that depend on a parameter with values in a topological space. These mappings are assumed to be continuously differentiable for each value of the parameter. Under normality (regularity) assumptions of the mappings under consideration, we obtain sufficient conditions for the existence of global and semilocal implicit functions. A priori estimates for solutions are given. As an application of these results, we obtain, in particular, a theorem on extending an implicit function from a given closed set to the whole parameter space and a theorem on coincidence points of mappings.Bibliography: 32 titles.

中文翻译：

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Banach 空间中隐函数和反函数的全局定理和半局部定理

我们考虑两个 Banach 空间之间的连续映射，这取决于拓扑空间中具有值的参数。假设这些映射对于参数的每个值都是连续可微的。在所考虑映射的正态性（规律性）假设下，我们获得了全局和半局部隐函数存在的充分条件。先验给出了解决方案的估计。作为这些结果的应用，我们特别得到了一个关于将隐函数从给定闭集扩展到整个参数空间的定理和一个关于映射重合点的定理。参考书目：32 题。