In this paper we study a functional equation of linear combination of nonautonomous iterations, which can be reduced from invariance of an interval homeomorphism under nonautonomous iteration. We discuss existence, uniqueness and continuous dependence for increasing Lipschitzian solutions on a compact interval, and also discuss for bounded increasing Lipschitzian solutions and unbounded ones on the whole $ \mathbb{R} $.

中文翻译：

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非自治迭代泛函方程的区间同胚解

在本文中，我们研究了非自治迭代的线性组合的函数方程，该方程可以通过非自治迭代下的区间同胚性的不变性来减少。我们讨论了在紧致区间上增加Lipschitzian解的存在性，唯一性和连续依赖性，还讨论了在整个$ \ mathbb {R} $上有界增加Lipschitzian解和无界解决方案。