3
$\begingroup$

I have done some research on the internet about the inequality called Holder, but I've encountered some explanations in sites like Turkis Math Wikipedia or Wolfram but none of those explanations were helpful enough, I want to be able to define what Holder's Inequality is and solve inequality questions using Holder's, I need an elementary level explanation, I do not know integrals, I am not very well informed about series (at least in some level), I am a Turkish high school student in preparation for Maths Olympiad, so I know about Cauchy-Schwarz, AM-GM and all these other concepts, if I am not advanced enough to understand the definition of it or put it to application, what topics should I study first?

What are your suggestions?

Thank you:)

$\endgroup$

closed as off-topic by GAVD, José Carlos Santos, Namaste, JMP, Xander Henderson Sep 25 '17 at 1:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – GAVD, José Carlos Santos, Namaste, JMP
If this question can be reworded to fit the rules in the help center, please edit the question.

4
$\begingroup$

For Math Olympiad purposes you just need basic algebra to understand Hölder's inequality, so if you're familiar with means inequalities and Cauchy-Schwarz you're just fine.

Anyway, this is Hölder's inequality, as I know it. Let $p$, $q$ be positive real numbers such that $\frac{1}{p} + \frac{1}{q} = 1$. Also, let $a_1, \: \dots, \: a_n$ and $b_1, \: \dots, \: b_n$ be nonnegative real numbers. Then $$\sum_{i = 1}^n a_ib_i \le \left(\sum_{i = 1}^n a_i^p\right)^{1/p} \left(\sum_{i = 1}^n b_i^q\right)^{1/q}$$

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.