# Tags: functional equations and functional inequalities

The tag was recently created. Since there are likely some previous questions on such a topic, some retagging will already be needed whichever way this discussion goes.

I am wondering whether we should collect both that and under one heading. The main consideration, I expect is whether functional equations and functional inequalities require different or the same tools?

Also, if it is decided that they should be under one heading, what should the tag name be?

• Perhaps we should collect them both under functional-equations? Or perhaps we feel this is too misleading? – davidlowryduda Mod May 30 '12 at 13:01
• That's the main worry: while we can try to clarify in the tag wiki, I wonder if there is a better, less misleading name available for the subject. – Willie Wong May 30 '12 at 13:02
• And in fact, "inequalities" is technically broader (and includes) "equations", which is just a two-way inequality... – Willie Wong May 30 '12 at 13:03
• If I had wanted to suggest that, I would have suggested it. While technically "inequalities" $\supset$ "equalities", it does carry certain connotations. – Willie Wong May 30 '12 at 13:09
• Would question on Minkowski inequality and similar inequalities fall under this tag? Many questions on convex functions could be perhaps understood as questions on functional inequalities. – Martin Sleziak May 30 '12 at 14:17
• @Martin: I imagine there to be a difference between "finding functions that satisfy inequality blah" and "demonstrating a function satisfies inequality blah". – Willie Wong May 30 '12 at 14:19
• Here's a sample of questions which might fall into that tag - if we decide to create one. 1 2 3 4 5 – Martin Sleziak May 30 '12 at 14:22
• We don't consolidate (equalities) and (inequalities), why consolidate the functional versions? – Nick Alger May 30 '12 at 20:31

## 1 Answer

I believe that in many cases methods used for functional equations and inequalities use similar results and some results for functional equations have analogues for functional inequalities. See e.g. the book Marek Kuczma: An Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation and Jensen's Inequality.

So I think that the best solution would be to use the same tag for both functional equations and functional inequalities. Since this might be confusing for some posters (most of the people probably don't check tag-wiki), I propose to keep tag, but make it a synonym of .

Question related to the proposal: Only the users which have some rep in the tag can vote to make that a synonym. At the moment contains only one question and there is no answer to it. So there are no users that could upvote the proposal to make the two synonymous, so there is a technical problem with my suggestion.

Is there something mods can do about this? Can mods make synonyms without users having to upvote the proposed synonym?

But it was explained in Willie Wong's comment bellow that a moderator can make synonyms, so there is a way to bypass this problem (if we decide to use this solution).

• yes. Mods can make synonyms. So if you drum up enough support here I'll be happy to make the synonym. – Willie Wong May 31 '12 at 8:50