We consider set-valued mappings acting in metric spaces and show that, under natural general assumptions, the set of coincidence points of two such mappings one of which is covering and the other is Lipschitz continuous is dense in the set of generalized coincidence points of these mappings. We use this result to study the coincidence points and generalized coincidence points of a set-valued covering mapping and a set-valued Lipschitz mapping that depend on a parameter. In particular, we obtain conditions that guarantee the existence of a coincidence point for all values of the parameter under the assumption that a coincidence point exists for one value of the parameter.

中文翻译：

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两个集值映射的重合点和广义重合点

我们考虑了作用于度量空间的集值映射，并表明，在自然的一般假设下，两个这样的映射的重合点集（其中一个是覆盖的，另一个是Lipschitz连续）在这些重合点的集合中是密集的映射。我们使用此结果来研究依赖于参数的集值覆盖映射和集值Lipschitz映射的重合点和广义重合点。尤其是，我们获得了在参数的一个值存在一个重合点的前提下保证该参数的所有值都存在一个重合点的条件。