query: Prove that a function is constant.
positive_passages.docid: 142138
positive_passages.text: Show that $f(x)$ is a constant function if $\lim\limits_{h\to 0}\frac{1}{h^3}\int_{-h}^{h}f(x+t)\cdot t\,dt=0$ for all $x$
negative_passages.docid: 57180
negative_passages.text: Techniques to prove a function is uniformly continuous
negative_passages.docid: 14578
negative_passages.text: Proving that an additive function $f$ is continuous if it is continuous at a single point
negative_passages.docid: 27772
negative_passages.text: Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.
negative_passages.docid: 153191
negative_passages.text: A function satisfy $x\frac{\partial f(x,y)}{\partial x}+y\frac{\partial f(x,y)}{\partial y}=0$ in a convex domain implies it is a constant
negative_passages.docid: 93270
negative_passages.text: is that function must be constant under the following conditions
negative_passages.docid: 7878
negative_passages.text: Proving that a doubly-periodic entire function $f$ is constant.
negative_passages.docid: 114245
negative_passages.text: What might I use to show that an entire function with positive real parts is constant?
negative_passages.docid: 776
negative_passages.text: Entire function with positive real part is constant (no Picard)
negative_passages.docid: 132478
negative_passages.text: Prove that continuous functions mapping irrationals to rationals must be constant
negative_passages.docid: 8179
negative_passages.text: If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
negative_passages.docid: 20273
negative_passages.text: Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
negative_passages.docid: 62640
negative_passages.text: Show a given analytic function is constant
negative_passages.docid: 158407
negative_passages.text: derivative bounded by a constant multiple of the function
negative_passages.docid: 89050
negative_passages.text: If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
negative_passages.docid: 9451
negative_passages.text: Show bounded and convex function on $\mathbb R$ is constant
negative_passages.docid: 5416
negative_passages.text: How does one prove if a multivariate function is constant?