Solving iterative functional equations for a class of piecewise linear -functions

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• 作者：Roman Geiselhart ; Fabian Wirth
• 关键词：Iterative functional equations ; Piecewise linear and K&infin ; K&infin ; -functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：15 March, 2014
• 年：2014
• 卷：411
• 期：2
• 页码：652-664
• 全文大小：377 K

文摘

We consider the problem of solving functional equations in , the space of homeomorphisms of . The problem is treated for the subclass of continuous functions that are defined as affine functions on a countable partition of and for which the partition has no accumulation of intervals from the right. Within this class it can be shown that the problem has a unique solution. The proof is constructive and can be implemented numerically. Some properties of solutions are discussed.