Lipschitz Dependence of Bounded Smooth Solutions for a Class of Second Order Iterative Function Equations
In order to study the Lipschitz dependence of C1 bounded smooth solutions of a class of second-order iterated functional equations on known functions at a definite bounded distance on C1,a Lipschitz condition is imposed on the derivatives of the known functions and a new metric is introduced,which represents the relationship between the original function and the derivative function.The Lipschitz dependence on the known function is proved on the basis of the relevant lemmas giving the derivation of the Lipschitz dependence,and the lemmas are applied to compute the distance between smooth solutions of the iterated functional equation.
a class of second order iterative functional equationcontinuous functionsmooth solutionLipschitz dependency
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