New posts in cauchy-schwarz-inequality

For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$

Proof for Cauchy-Schwarz inequality for Trace [closed]

Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $ [duplicate]

Intuition for the Cauchy-Schwarz inequality that does not rely on a geometric interpretation of vectors

Inequality $\sum\limits_{k=1}^n \frac{1}{n+k} \le \frac{3}{4}$

How to prove this inequality involving $\tanh$?

AM-GM inequality: $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{d} + \frac{d^2}{a} \geq a + b + c + d$

proving :$\frac{ab}{a^2+3b^2}+\frac{cb}{b^2+3c^2}+\frac{ac}{c^2+3a^2}\le\frac{3}{4}$.

Verfication of deduction made using the Cauchy-Schwarz inequality

Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$

How to find the minimum value of this function?

How to prove that $\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq\frac{3\sqrt{3}}{4}$?

Generalization of Cauchy-Schwarz/Hölder inequality

Inequality in cyclic order : $\sum\frac{8}{(a+b)^2+4abc}+a^2+b^2+c^2\ge\sum\frac{8}{a+3}$ [closed]

Hard inequality for positive numbers

Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Is the following generalization of Cauchy-Schwarz inequality true?

Stronger than Nesbitt's inequality $\frac{a}{\sqrt[4]{8(b^4+c^4)}}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}$

Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$