Intereting Posts

Four balls with different colors in a box, how many times do I need to pick to see all four colors?
Polynomial $p(x) = 0$ for all $x$ implies coefficients of polynomial are zero
Convergence of $\sum_{n=2}^\infty \frac{1}{n^\alpha \ln^\beta (n)} $
Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$
cubic root of negative numbers
Rigorous Proof?: Proving Cauchy Criterion of Integrals
What is the real life use of hyperbola?
Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
normal distribution hazard rate increasing function
Least squares problem: find the line through the origin in $\mathbb{R}^{3}$
How to define countability of $\omega^{\omega}$ and $\omega_1$? in set theory?
Find Cartesian equation of $r=\theta$
What is the negation of this statement?
Ring homomorphisms from $\Bbb Q$ into a ring
Use Stokes's Theorem to show $\oint_{C} y ~dx + z ~dy + x ~dz = \sqrt{3} \pi a^2$

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?

- The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
- Differentiable $f$ such that the set of translates of multiples of $f$ is a vector space of dimension two
- Spectrum of symmetric, non-selfadjoint operator on Hilbert space
- Simplicity and isolation of the first eigenvalue associated with some differential operators
- About a weak topology on TVS
- $H^{-1}(\Omega)$ given an inner product involving inverse Laplacian, explanation required
- How can I visualize the nuclear norm ball
- Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?
- On a manifold, is the $L^p$ space of vector fields complete?
- Standard compactness argument

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.

- Problem in understanding p implies q
- Elliptic regularization of the heat equation
- Problem about jointly continuous and linearity of expectation.
- Find by integrating the area of the triangle vertices $(5,1), (1,3)\;\text{and}\;(-1,-2)$
- Hausdorff Dimension of a manifold of dimension n?
- Find the volume of the largest right circular cone that can be inscribed in a sphere of radius r?
- General solution of second-order linear ODE
- Give examples of compact spaces $A,B$ such that $A\cap B$ is not compact
- upper bound on partial sums of Dirichlet character
- “sheaf” au sens de Serre
- lemma: Cauchy sequences are bounded.
- Why is the complex plane shaped like it is?
- Can $18$ consecutive integers be separated into two groups,such that their product is equal?
- Existence of isomorphism between tensor products.
- Cauchy Sequences are Bounded. Questions on proof (Abbott p 59 lemma 2.6.3)