query: $U$ is convex, $f\in H(U)$ and $|f'(z)-1|<1, \forall z\in U$ then $f $ is one-one function
positive_passages.docid: 18763
positive_passages.text: injective holomorphic function on a convex set
negative_passages.docid: 95288
negative_passages.text: Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$.
negative_passages.docid: 125175
negative_passages.text: convexity proof of a function including ln and sums
negative_passages.docid: 116382
negative_passages.text: Showing convexity of a function with the restriction over an arbitrary line
negative_passages.docid: 64197
negative_passages.text: Subgradients of non-convex functions
negative_passages.docid: 99827
negative_passages.text: For what values will f(x) be necessarily one-one?
negative_passages.docid: 92029
negative_passages.text: Is this rational function convex?
negative_passages.docid: 14448
negative_passages.text: Elementary proof that $|x|^p$ is convex.
negative_passages.docid: 9451
negative_passages.text: Show bounded and convex function on $\mathbb R$ is constant
negative_passages.docid: 91980
negative_passages.text: Prove that f is one-to-one on D
negative_passages.docid: 118136
negative_passages.text: Finding univalent function with $f(z_1)=z_2$
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 80559
negative_passages.text: In $C[0,1]$ prove that the subset of Lipschitz functions is dense
negative_passages.docid: 5365
negative_passages.text: Bound on $|f'(0)|$ of a holomorphic funtion in the unit disk
negative_passages.docid: 116548
negative_passages.text: How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).
negative_passages.docid: 158561
negative_passages.text: Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is
negative_passages.docid: 10181
negative_passages.text: Entire one-to-one functions are linear