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Results tagged with real-analysis
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user 25619
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
8
votes
Existence of function satisfying $f(f'(x))=x$ almost everywhere
Looking for a solution of the form $f(x)=ax^b$, $x>0$, one finds
$$
a = \phi^{-\phi/(\phi+1)}, ~~~ b=\phi
$$
where $\phi=\frac{\sqrt{5}+1}{2}$ is the Golden ratio.
- 664
1
vote
1
answer
331
views
Quadratic Convergence in Fixed Point Iteration
Quadratic convergence is the hallmark of Newton's Method for root-solving. I'm looking for a result that implies the Newton result that looks like this:
Theorem : Let $f:\mathbb{R}^n\rightarrow\mathb …
- 664