Questions on proving, manipulating and applying inequalities. Do not use this tag just because an inequality appears somewhere in your question.
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Sobolev estimates $||\phi||_2\leq||\phi||_{H^2}$
I have been reading the paper 'Convergence of a finite volume scheme for a system of interacting species with cross-diffusion' by Carrillo et al. in Section 4.1 they have been using an estimate, $||\... functional-analysis inequality lp-spaces sobolev-spaces- 606
System of inequations
If $p$, $q$, $r$, $s$ and $t$ are real numbers such that $q+r<s+t$, $r+s<t+p$, $s+t<p+q$ and $p+q<r+s$, then find the largest and the smallest term among them. This is how I solved it: $$... algebra-precalculus inequality systems-of-equations- 339
What would be a good metric that puts heavier weight on a longer time period?
I'm currently trying to think of a metric to measure a performance of a product that gives higher points to longer contracts. For example, let's say that one contract A is a year long contract and the ... inequality logarithms fractions applications- 1
Inequality with discriminants
If $x^2-ax+1-2a^2>0$ for all $x \in {R}$, find range of $a$ The solution to this takes the discriminant of the expression in terms of $a$, i.e., $$\implies D={a^2-4(1-2a)}>0(\because x \in R)$$ ... algebra-precalculus inequality polynomials quadratics- 339
Inequality about $x^p$ for $p\geq 2$ a real number
I am stuck with the following inequality $$g^2(n+2)+2g(n+2)g(n)-g^2(n+1)-2g(n+1)g(n+2)\geq 0,$$ for all integer $n\geq 1$. Here, $g(x)=x^p$ where $p\geq 2$ is a real number. I need help. analysis inequality convex-analysis- 21
The relationship of the $l^1$ norm to other norms
For a vector there are different norms, such as the $l^1$ norm, the $l^2$ norm and the $l^p$ norm, and there is a relationship between the $l^1$ and $l^2$ norms as follows:$\Vert x \Vert_1 \leq \sqrt{... inequality numerical-methods vectors- 1
Show: $\prod_i t_i^{w_it_i} \geq \Big( \frac{\sum_i w_it_i}{\sum_i w_i} \Big)^{\sum_i w_it_i}$
Let $w_i$ be $k$ weights and $t_i$ be k numbers s.t. $w_i , t_i \geq 0$. Then prove that: \begin{align*} \prod_i t_i^{w_it_i} \geq \Big( \frac{\sum_i w_it_i}{\sum_i w_i} \Big)^{\sum_i w_it_i} \end{... inequality contest-math- 2,143
Let $f(x)=\frac{x}{e^x}$, and $f(a)=f(b), a<1<b$. How to prove that $\frac{a^2}{a-1}+\frac{b^2}{b-1}>\frac{10}{3}$?
Let $f(x)=\frac{x}{e^x}$, and $f(a)=f(b), a<1<b$. How to prove that $\frac{a^2}{a-1}+\frac{b^2}{b-1}>\frac{10}{3}$? I think to use a derivative but I don't know how? real-analysis inequality- 6,185
Combinatorial proof of a simple inequality
I want to prove the following inequality combinatorialy $$\left(\frac{n+1}{2}\right)^n \ge n! ,n \in \mathbb{N} $$ my attempts in this direction so far have been $$\left(\frac{n+1}{2}\right)^n \ge n! \... combinatorics inequality combinatorial-proofs- 221
Does $\int_0^1 f(x) dx < f(0)$ make sense? [closed]
Let $f$ be a continuous function on the interval $[0, 1]$, $f(x) < 0$ for all $x \in [0,1]$. Then does the following inequality hold: $$\int_0^1 f(x) dx < f(0).$$ calculus integration inequality- 757
I not understanding a cancellation step in Spivak proof.
There is a question about this exact same proof but the answer is not satisfying me so I'm going to run it again if you don't mind. I will post the original question after mine. In his chapter on ... calculus algebra-precalculus limits inequality absolute-value- 1,292
if $(a_n)_{n=1}^\infty$ converges to $c$, then $c$ is a limit point of $(a_n)_{n=1}^\infty$ and, in fact, the only one.
if $(a_n)_{n=1}^\infty$ converges to $c$, then $c$ is a limit point of $(a_n)_{n=1}^\infty$ and, in fact, the only one. I already proved what concerns that $c$ is a limit point, nonetheless I'm stuck ... real-analysis calculus analysis inequality- 147
Schwarz inequality and general proof
Recently I've learn about the Cauchy-Schwarz inequality. So, as we all know this this inequality states that for an inner product vector space for all vectors $x, y$ we have that: $|\langle x,y\... inequality vector-spaces inner-products cauchy-schwarz-inequality- 59
Maximum value of $ \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} $ in triangle is... [duplicate]
I was asked to prove the given inequality in a triangle Prove that $\displaystyle \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} < 2 $ As one of the side approaches to zero the remaining two sides ... inequality optimization triangles- 127
Is it possible to prove $\|f(x)-g(y)\| \le M\|x-y\|$?
Setting/Question Let $(X,\|\cdot \|)$ be a normed vector space and $f:X→X$ and $g:X→X$ both linear, bounded, and bijective operators each. I would like to prove or disprove $$\|f(x)-g(y)\| \le M\|x-y\... inequality normed-spaces- 31
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