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Apr
11
awarded  Mortarboard
Apr
7
comment Fake proof: Equivalence of norms
$\mu$ depends on $f$ while $\alpha$ should not depend on $f$ but it does if you want to fulfill your last inequality.
Apr
5
answered (Updated) Geometric Illustration of Monotone and Maximal Monotone Maps
Apr
5
comment (Updated) Geometric Illustration of Monotone and Maximal Monotone Maps
You need to be more specific. What is a "geometric illustration" as well as an "excellent example" for you? You want only maximal monotone operators in finite dimensions? The literature on maximal monotone operators is extremely broad.
Mar
12
comment arclength parametrization intuition
The speed of drawing the curve in the standard parametrization is $1$.
Mar
7
answered Why is $(T + N_X)(x) \subset T(x)$ when $Dom T \subset X$?
Mar
6
comment Closure of the interior of the epigraph
Yes, the closure of the non-empty interior of a closed convex set is the set itself in any linear topological space. You can find this result in Holmes: "Geometric Functional Analysis and its Applications" on p. 59 and its proof is based on the continuity of the operations.
Feb
18
answered Non-linear analysis
Feb
17
revised Example of maximal monotone operators in non-reflexive Banach spaces with applications in PDE
added 100 characters in body
Feb
12
comment Example of maximal monotone operators in non-reflexive Banach spaces with applications in PDE
Of course any subdifferential is maximal monotone and is involved in variational inequalities (in any Banach space). What about examples that do not depend on the subdifferential?
Feb
12
asked Example of maximal monotone operators in non-reflexive Banach spaces with applications in PDE
Feb
6
revised Continuity of the dual product reloaded
deleted 21 characters in body
Feb
6
comment Continuity of the dual product reloaded
@DanielFischer You're right. I modified it so it holds. It seems that your argument also holds for non-reflexive spaces. Please write it as an answer.
Feb
6
revised Continuity of the dual product reloaded
added 76 characters in body
Jan
18
awarded  Fanatic
Jan
13
asked Continuity of the dual product reloaded
Jan
13
comment Is my proof that if $x_n$ is a sequence such that $x_n \rightarrow +\infty$ then $(1+\frac{1}{x_n})^{x_n}\rightarrow e$ correct?
Is $x_n$ an integer?
Jan
12
comment Is my proof that if $x_n$ is a sequence such that $x_n \rightarrow +\infty$ then $(1+\frac{1}{x_n})^{x_n}\rightarrow e$ correct?
Your solution is not correct. Maybe take a look at how you prove that $(1+1/n)^n\to e$ and try from there.
Jan
11
awarded  Yearling
Jan
11
comment Is the biconjugate of a continuous functions also continuous?
@Quickbeam2k1 I was talking about $f^{**}$ which can be identically $-\infty$. You still have to show that $f^{**}$ is proper. Convex Analysis by R.T. Rockafellar Theorem 10.1 p.82 has the finite dimensional case.