Intereting Posts

(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
Is there exist a homemoorphism between either pair of $(0,1),(0,1],$
Bounds on $f(k ;a,b) =\frac{ \int_0^\infty \cos(a x) e^{-x^k} \, dx}{ \int_0^\infty \cos(b x) e^{-x^k}\, dx}$
Proving the total number of subsets of S is equal to $2^n$
What is the intuition behind the Poisson distribution's function?
Is the function $ f(x,y)=xy/(x^{2}+y^{2})$ where f(0,0) is defined to be 0 continuous?
sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
Approximating a Hilbert-Schmidt operator
The order of the number of integer pairs satisfying certain arithmetical function relationships
Finiteness of the number of big jumps of a Lévy process on a finite interval
Induction for recurrence
Examples for almost-semirings without absorbing zero
Calculating probability with n choose k
equation of a curve given 3 points and additional (constant) requirements
Coefficients of a polynomial also are the roots of the polynomial?

If $f:\mathbb{R}\to\mathbb{X}$ is a function from the real numbers to any normed vector space (finite or infinite dimension), and $f$ is Gateaux differentiable, is $f$ necessarily Frechet differentiable?

- Example of a closed subspace of a Banach space which is not complemented?
- Isometric to Dual implies Hilbertable?
- Relationship between $C_c^\infty(\Omega,\mathbb R^d)'$ and $H_0^1(\Omega,\mathbb R^d)'$
- Sum of closed spaces is not closed
- What is $L^p$-convergence useful for?
- Topologies of test functions and distributions
- Fourier Inversion formula on $L^2$
- Wave Operators: Calculus
- Why $C_0^\infty$ is dense in $L^p$?
- Weighted Poincare Inequality

Yes. In short, what differentiates (pardon the pun) Gateaux and Frechet is that derivatives in Frechet converge uniformly in the direction in the domain, while Gateaux asks only that the directional derivatives converge. Since there is only one `direction’ in the domain $\mathbb R$, these notions coincide in your case.

- Total number of unordered pairs of disjoint subsets of S
- Inhomogeneous 2nd-order linear differential equation
- Deriving the Airy functions from first principles
- Correspondences between Borel algebras and topological spaces
- Prove or disprove: $\sum_{n=0}^\infty e^{-|x-n|}$ converges uniformly in $(-\infty,\infty)$
- Why finite structures are uniquely characterized?
- How come that two inductive subsets can be different
- Basis of the space of linear maps between vector spaces
- Determining origin of norm
- Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$
- Evaluating $\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$
- What is a Limit?
- Prop 12.8 in Bott & Tu
- if $AB\neq 0$ for any non zero matrix $B$ then $A$ is invertible
- Could you recommend some classic textbooks on ordinary/partial differential equation?