## Continuous solutions of a second order iterative equation. (arXiv:1803.03770v1 [math.CA])

In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to those given functions, we prove the existence of continuous solutions on the whole \$\mathbb{R}\$ by applying the contraction principle. In the case without Lipschitz conditions we hardly use the contraction principle, but we construct continuous solutions on \$\mathbb{R}\$ recursively with a partition of \$\mathbb{R}\$. 查看全文>>