Higher regularity of solutions of an iterative functional equation
Abstract
In this paper, we investigate the existence of Cn, n∈ N+, solutions for a class of second-order iterative functional equations involving iterates of the unknown function and a nonlinear term. Applying the Fiber Contraction Theorem and Fa\`a di Bruno's Formula, we establish the existence of bounded Cn solutions with bounded derivatives of order from 1 to n.
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