平均型映射与不变原理
Mean-type mappings and invariance principle
摘要：
在有限维情形下，研究了平均型映射及其不变平均，以及不变平均的唯一性与映射轨道收敛性之间的关系。特别是它示出，不变性平均的唯一性意味着所有轨道的收敛。构造了一个强非正则平均型映射，并确定了它的唯一不变平均。并给出了在求解一个函数方程中的应用。
英文摘要：
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an invariance mean implies the convergence of all orbits. A strongly irregular mean-type mapping is constructed and its unique invariant mean is determined. An application in solving a functional equation is presented.
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