Non-monotonic solutions and continuously differentiable solutions of conjugacy equations |
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Authors: | Yong-Guo Shi |
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Institution: | Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan 641112, PR China |
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Abstract: | 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. |
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Keywords: | Functional equation Conjugacy equation Non-monotonic solution Continuously differentiable solution |
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