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Jun
5
asked Calculating the convex conjugate of the function $f(x)=\lim_{n\to \infty}\left(-\frac{1}{n}\log \sum_{k=1}^n e^{a_k\cdot x+b_k}\right)$.
Jun
5
asked Legendre–Fenchel transformation $ f^{\ast}(x^\ast)=\sup_{x\in\mathbb{R}^n}\{\langle x,x^\ast\rangle -f(x)\} $
May
13
answered $ d(x,y)^2 \le d(x,z)^2 - d(y,z)^2\color{}{+\varphi\big(x,y,z,d(x,y),d(y,z) \big)}? $
Apr
5
answered If $f$ is a continuous function such that $|f(x+y)-f(x)-f(y)|$ is bounded and $f(n)=o(n)$, then $f$ is bounded
Apr
4
answered If $\lim_{x\to0} f(x)+g(x)$ and $\lim_{x\to0} f(x)g(x)$ exist simultaneously, are there any $f(x)$ and $g(x)$ that do not have limit
Apr
2
asked Number of circuits that surround the square.
Mar
18
answered When a function contains a sequence, and how to find the function's limit?
Mar
12
asked Proof of Banach's homeomorphism theorem without the contraction map principle.
Mar
6
asked Inverse Function Theorem. On the classical method of proof.
Feb
7
answered Prove/disprove: $\forall f\ \in \mathbb N ^{\mathbb R}. \forall x\in \mathbb R. \exists y\in \mathbb R ((f(x)=f(y))\wedge (x\neq y))$
Feb
1
answered Properties of sup and lim inf.
Jan
31
answered $ \sum_{n=1}^{\infty}a_{n} $ diverges but $ \sum_{n=1}^{\infty}\frac{a_{n}}{1+a_{n}^{2}} $ sometimes converges and sometime diverges.
Jan
13
answered convergence of $\prod_{n=1}^\infty (1-\frac{z}{n!})$
Jan
3
answered C*-algebras: Literature?
Jan
2
answered Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
Jan
1
asked $ \|u(x)+u(x)-x +o(\|x\|^p)\|<r $?
Dec
27
asked $ C^p_0(B,\mathbb{X})$ is a Banach space with the norm of $C^p\!\!$-topology?
Dec
26
answered If $f'(z_0)\neq 0$ then $f$ is one to one on some open disk $D_r(z_0)$
Dec
9
answered Set notation equivalence of AND & OR
Dec
2
answered The inverse of a bijective holomorphic function