Blog

In the paper (http://www.sciencedirect.com/science/article/pii/S0022247X97953439), Webster obtained a unique solution of the functional equation $ f(x+1)=g(x)f(x)$ (where $ f,g:\mathbb{R}^+\rightarrow \mathbb{R}^+$ ) under some conditions one of which is $ \lim_\limits{x\to \infty}\frac{g(x+w)}{g(x)}=1$ for all $ w>0$ . Now, I’m looking for a function $ g:\mathbb{R}^+\rightarrow \mathbb{R}^+$ such that the sequence $ \frac{g(n+1)}{g(n)}\rightarrow 1$ , $ \lim_\limits{x\to \infty}\frac{g(x+w_0)}{g(x)}$Read more