query: $f:D \rightarrow \mathbb C$ holomorphic, $D$ a convex set, $Re(f'(z))>0$. Prove that $f$ is injective
positive_passages.docid: 597
positive_passages.text: f is differentiable on convex domain D and Re(f')>0 implies f is injective on D
negative_passages.docid: 124346
negative_passages.text: Where is $f(z)=\Re (z)$ differentiable?
negative_passages.docid: 103125
negative_passages.text: Show that a non-constant holomorphic function has zeroes in a compact set
negative_passages.docid: 136818
negative_passages.text: There is a $C > 0$ such that $\vert f(z)-f(w)\vert \leq C\vert z-w\vert$ for a holomorphic map into $B(0, R)$.
negative_passages.docid: 74622
negative_passages.text: Composition of holomorphic functions is holomorphic
negative_passages.docid: 27251
negative_passages.text: Holomorphic function with $f\circ f=f$
negative_passages.docid: 20955
negative_passages.text: Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
negative_passages.docid: 147420
negative_passages.text: Equivalent definitions of convexity for $f\in\mathcal C^1(\mathbb R^n)$
negative_passages.docid: 125251
negative_passages.text: Show that a function from a Riemann Surface $g:Y\to\mathbb{C}$ is holomorphic iff its composition with a proper holomorphic map is holomorphic.
negative_passages.docid: 135577
negative_passages.text: Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
negative_passages.docid: 123467
negative_passages.text: Prove that $f(z) = e^z$ maps $\mathbb{C} \setminus B $ onto $\mathbb{C} \setminus \{0\}$.
negative_passages.docid: 112807
negative_passages.text: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
negative_passages.docid: 147270
negative_passages.text: Entire function. Prove that $f(\bar{z})=\overline{f(z)}, \forall z\in C$
negative_passages.docid: 62280
negative_passages.text: If $f:U\to V$ is holomorphic and $f'(z)\neq 0$ for all $z\in U$, then$f$ is locally bijective.
negative_passages.docid: 5365
negative_passages.text: Bound on $|f'(0)|$ of a holomorphic funtion in the unit disk
negative_passages.docid: 92056
negative_passages.text: An inequality on holomorphic functions
negative_passages.docid: 6098
negative_passages.text: Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$