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arXiv · 2105.08402

Differentiable solutions of an equation with product of iterates

Chaitanya Gopalakrishna
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Abstract

In the previous work [2] (i.e., arXiv:2105.03385), we considered continuous solutions of an iterative equation involving the multiplication of iterates. In this paper, we continue to investigate this equation for differentiable solutions. Similar to continuous solutions until [2], there is no obtained result on differentiable solutions of such an equation on non-compact intervals of $\mathbb{R}$. Although our strategy here is to use conjugation to reduce the equation to the well-known polynomial-like iterative equation as in [2], all known results on differentiable solutions of the latter are given on compact intervals. We re-explore polynomial-like iterative equation on the whole of R and prove the existence and uniqueness of differentiable solutions of our equation on $\mathbb{R}_+$ and $\mathbb{R}_-$.

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Chaitanya Gopalakrishna. 2021-05-18. Differentiable solutions of an equation with product of iterates. https://arxiv.org/abs/2105.08402

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