List questions from karamata-inequality

Published on 25 Mar 2026 - 6:29

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$(1+a_1)(1+a_2)...(1+a_n) \geq 1+a_1 + a_2 +...+a_n $

Published on 25 Mar 2026 - 6:28

399

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Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$

Published on 25 Mar 2026 - 6:30

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If a,b,c are sides of a triangle, prove: $ \sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \le \sqrt{a} + \sqrt{b} + \sqrt{c} $

Published on 25 Mar 2026 - 6:29

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How prove this inequality

Published on 10 Apr 2026 - 11:21

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Maximum of $x^3+y^3+z^3$ with $x+y+z=3$

Published on 10 May 2026 - 12:28

219

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How do I go about solving this equation? $3^x + 10^x = 4^x + 9^x$

Published on 25 Mar 2026 - 6:29

90

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Petrovic and Jensen inequaltiy

Published on 11 Apr 2026 - 1:42

492

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Upper bound for sum of exponentials

Published on 25 Mar 2026 - 6:31

62

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simple arithmetic inequality

Published on 10 Apr 2026 - 16:28

140

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Somebody help me please. I have a difficult inequality.

Published on 25 Mar 2026 - 6:27

105

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If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$

Published on 25 Mar 2026 - 6:30

127

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Find maximize and minimize of $P=x+y$

Published on 25 Mar 2026 - 6:31

35

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Whether $(a-k)^p-(a-h)^p\ge (h-k)^p$ for all $a>h>k>0 ,~ p\ge 1$?

Published on 25 Mar 2026 - 6:29

361

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Showing that $ 1<\sin\frac{\alpha}{2}+\sin\frac{\beta}{2}+\sin\frac{\gamma}{2}$

Published on 17 Apr 2026 - 7:56

List Question

Can we prove Am-GM Inequality using Karamata’s Inequality?

$(1+a_1)(1+a_2)...(1+a_n) \geq 1+a_1 + a_2 +...+a_n $

Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$

If a,b,c are sides of a triangle, prove: $ \sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \le \sqrt{a} + \sqrt{b} + \sqrt{c} $

How prove this inequality

Maximum of $x^3+y^3+z^3$ with $x+y+z=3$

How do I go about solving this equation? $3^x + 10^x = 4^x + 9^x$

Petrovic and Jensen inequaltiy

Upper bound for sum of exponentials

simple arithmetic inequality

Somebody help me please. I have a difficult inequality.

If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$

Find maximize and minimize of $P=x+y$

Whether $(a-k)^p-(a-h)^p\ge (h-k)^p$ for all $a>h>k>0 ,~ p\ge 1$?

Showing that $ 1<\sin\frac{\alpha}{2}+\sin\frac{\beta}{2}+\sin\frac{\gamma}{2}$

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