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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

3 votes
2 answers
1k views

convergence of infimum

I have a question during my intership. Given a convergent sequence of continuous et convex functions $\{f_n(x)\}$ defined in $\mathbb{R}^M$. These functions are uniformly Lipschitz continuous which me …
0 votes
1 answer
138 views

question about the closed form of a function

Hi everyone! I have a question about how to find the closed form of a function defined by $$\phi(\theta)=\inf_{x\geq 2}f(x;\theta)\equiv\inf_{x\geq 2}\frac{(x+2)^2}{\frac{1}{\theta}\left(\frac{x-1}{2 …
0 votes
0 answers
176 views

search for a function satisfying some conditions

Hi everyone, I would like to find a function $$\Psi\in\mathcal{C}^2: z\in\mathbb{R}\rightarrow\Psi(z)\in\mathbb{R_+}$$ satisfying the following conditions: $$1-\frac{z\Psi'(z)}{\Psi(z)}+8s\Psi''(z …