List questions from gateaux-derivative | MathQa

Show that a function is nowhere Gateaux differentiable.

Published on 12 Jan 2025 - 20:47

show that $(y^* \circ F) * \gamma(x) = \int_X {y^* \circ F(x+t)}d\gamma(t)$ is Gateaux differentiable everywhere

Published on 12 Jan 2025 - 21:02

Definition of $\nabla f(ux_n - S(t))$ on a Banach space

Published on 12 Jan 2025 - 20:42

Show that $f=1/2 ||T(x)||^2$ is Gateaux differentiable everywhere.

Published on 12 Jan 2025 - 20:50

Is $ \left| \lim_{t \rightarrow 0}{\frac{f(x+ty) - f(x)}{t}} \right| \leq \lim_{t \rightarrow 0}{ \frac{|f(x+ty) - f(x)|}{|t|}}$

Published on 12 Jan 2025 - 21:02

existence directional derivatives

Published on 12 Jan 2025 - 20:38

Show that $G(y^)(h) = \int \limits _X {y^ \circ F(t) \Bbb d \nu _h (t)}$ for some measure $\nu$ on $X$

Published on 12 Jan 2025 - 20:58

well defined $F(u)=\int_I \psi udx$ and it's Gateaux derivative is $DF(u)=\psi(u)$

Published on 12 Jan 2025 - 20:56

$F$ with Gateaux-derivative $A$, then $pF(u)=A(u)(u)$

Published on 12 Jan 2025 - 20:38

Is this function Gateaux differentiable?

Published on 12 Jan 2025 - 20:34