Non-monotonic solutions and continuously differentiable solutions of conjugacy equations
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摘要
In this paper solutions of conjugacy equation φ(f(x))=g(φ(x)) for a strictly decreasing continuous given function f and a continuous given function g (maybe non-monotonic) are constructed by piecewise defining. We determine the conditions for piecewise continuously differentiable solutions of conjugacy equations with a strictly decreasing continuously differentiable given function f and a continuously differentiable given function g. Finally, the recursive algorithm is implemented in MATLAB software and two examples are respectively presented for a non-monotonic solution and a continuously differentiable one.
论文关键词:Functional equation,Conjugacy equation,Non-monotonic solution,Continuously differentiable solution
论文评审过程:Available online 21 August 2009.
论文官网地址:https://doi.org/10.1016/j.amc.2009.08.031