Question

Prove or disprove the following generalization :$\sum_{i,j=1}^{n}f\left(a_{i}a_{j}\right)>n^{2}f\left(\sum_{i,j=1}^{n}\frac{a_{i}a_{j}}{n^{2}}\right)$

score 140 · Answer 1 · 2026-03-14 12:54:11

140

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Prove or disprove the following generalization :$\sum_{i,j=1}^{n}f\left(a_{i}a_{j}\right)>n^{2}f\left(\sum_{i,j=1}^{n}\frac{a_{i}a_{j}}{n^{2}}\right)$

Published on 14 Mar 2026 - 12:54

score 82 · Answer 2 · 2023-04-12 16:35:35

82

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Example of superreflexive space

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score 263 · Answer 3 · 2026-03-26 19:15:43

263

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Does there exist an infinite set admitting precisely four linear orders?

Published on 26 Mar 2026 - 19:15

score 226 · Answer 4 · 2023-04-14 17:21:06

226

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Does there exist an everywhere weakly continuous but nowhere strongly continuous function $f : [0,1] \to X$?

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score 73 · Answer 5 · 2023-04-15 09:53:36

73

Views

What $R$-modules $M$ and ideals $I$ satisfy $IM=M$?

Published on 15 Apr 2023 - 9:53

score 32 · Answer 6 · 2023-04-15 16:28:06

32

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Prove that the union of totally closed collections with respect union or intersection is not totally closed with respect union or intersection.

Published on 15 Apr 2023 - 16:28

score 62 · Answer 7 · 2026-03-28 06:00:31

62

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Could you provide me with an example of a group which has elements $a, b$ and $c$ such that the order of $abc$ is different from the order of $acb$?

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score 25 · Answer 8 · 2023-04-20 18:03:51

25

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Prove that if $\mathcal C⊆\mathcal P(X)$ is totally closed with respect intersection then $p_f[\cal C]$ isn't totally closed with respect intersection

Published on 20 Apr 2023 - 18:03

score 56 · Answer 9 · 2023-04-20 21:53:57

56

Views

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score 57 · Answer 10 · 2026-04-03 03:36:56

57

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score 75 · Answer 11 · 2026-03-25 22:30:44

75

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Need help with finding a counterexample to: if $2^h=coeq(2^{q_1}, 2^{q_2}).$ then $h=eq(q_1,q_2)$

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score 31 · Answer 12 · 2026-04-03 20:29:19

31

Views

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score 64 · Answer 13 · 2023-04-29 15:43:16

64

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score 73 · Answer 14 · 2026-03-28 08:36:35

73

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score 62 · Answer 15 · 2026-03-31 03:57:04

62

Views

How to give a counterexample of this estimate related to Paley-Littlewood theorem?

Published on 31 Mar 2026 - 3:57

List Question

Prove or disprove the following generalization :$\sum_{i,j=1}^{n}f\left(a_{i}a_{j}\right)>n^{2}f\left(\sum_{i,j=1}^{n}\frac{a_{i}a_{j}}{n^{2}}\right)$

Example of superreflexive space

Does there exist an infinite set admitting precisely four linear orders?

Does there exist an everywhere weakly continuous but nowhere strongly continuous function $f : [0,1] \to X$?

What $R$-modules $M$ and ideals $I$ satisfy $IM=M$?

Prove that the union of totally closed collections with respect union or intersection is not totally closed with respect union or intersection.

Could you provide me with an example of a group which has elements $a, b$ and $c$ such that the order of $abc$ is different from the order of $acb$?

Prove that if $\mathcal C⊆\mathcal P(X)$ is totally closed with respect intersection then $p_f[\cal C]$ isn't totally closed with respect intersection

Why does Mergelyan's theorem fail in higher dimensions?

How to compare number strings in terms of both sequential order of elements and rank order of values

Need help with finding a counterexample to: if $2^h=coeq(2^{q_1}, 2^{q_2}).$ then $h=eq(q_1,q_2)$

Functions that have their second derivatives as a lipschitz function

A uniformly convex normed vector space which is not reflexive

An example of dense subspace of $\ell_2$

How to give a counterexample of this estimate related to Paley-Littlewood theorem?

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