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