# Tagged Questions

0answers
29 views

### A basic question about upper hemicontinuity

Given a correspondence $f:X\rightarrow 2^X$, suppose X is a closed simplex in $\mathbb{R}^n$, and $f$ is compact-valued. We say $f$ is upper hemicontinuous if, $\forall x\in X$ and every open subset ...
0answers
44 views

2answers
130 views

### Limit of a sequence of fixed points also a fixed point?

Suppose I have a continuous function $f : [0,1]^n \rightarrow [0,1]^n$ (maybe $n$ is infinite). Suppose I have a sequence $\{a_n\}_{n=1}^\infty$ of points in $[0,1]^n$ where each $a_n$ is a fixed ...
3answers
283 views

### Prove the sequence $x_n = \frac{x_{n-1}}{2}+\frac{A}{2x_{n-1}} \rightarrow \sqrt{A}$ as $n \to \infty$

Show that if A is any positive number, then the sequence defined by: $$x_n = \frac{x_{n-1}}{2}+\frac{A}{2x_{n-1}}$$ for any $n \geq 1$ converges to $\sqrt{A}$ whenever $x_0 > 0$.
2answers
115 views

### Question on fixed point

I had some trouble to approach the question above. Especially (2) and (3). I appreciate if you can help!
2answers
274 views

3answers
405 views

### Finding the fixed points of a contraction

Banach's fixed point theorem gives us a sufficient condition for a function in a complete metric space to have a fixed point, namely it needs be a contraction. I'm interested in how to calculate the ...