Some open access journals, like Integers for example, don't charge the author any fee for publishing their article. Other open access journals do charge the author a fee and the author has to pay the fee so that their work can be posted online. Are there any trustworthy fee-based open access journals?
1Virtually all mathematics journals have fairly liberal policies about allowing authors to post preprints (and in many cases even the published paper) on repositories and personal websites. (This is not an answer to the question, but may be useful to those who arrive at this page).– David KetchesonMar 23, 2015 at 12:07
I'll try to link to pages which describe the open-access policy of the respective journals.
Both Proceedings of the AMS and Transactions of the AMS allow the author to pay a fee to make their article freely available electronically from the journal. If the author chooses not to pay the fee then the article is not freely available from the journal (but the author may post the final preprint on the arXiv or their personal website).
The (few) Elsevier journals I have looked at have a similar fee for publishing open-access. One example of which is the Journal of Mathematical Analysis and Applications. You might try their Journal Finder, which has a checkbox to only search for journals with open-access options.
Springer offers a similar program for some of its subscription-based journals which they call Open Choice. Not all of its journals have this option (e.g. Acta Mathematica doesn't).
We also note that Elsevier and Springer both publish a number of purely open-access journals, but I can't comment on their "trustworthiness".
You may need to view the last Springer link in incognito mode (or equivalent) if Springer's website keeps you logged in from your institution. This will ensure that only those journals which are completely open-access will be shown. Mar 23, 2015 at 0:50
Acta Mathematica is no longer a Springer journal and is now open access with $0 fee. Aug 8, 2019 at 22:02
While fees are unusual for Math open access journals (and I would initially suspect any journal charging them), there are trustworthy fee-charging journal, e.g. Pi and Sigma (http://journals.cambridge.org/action/displaySpecialPage?pageId=3896).
6Note that at present, Pi and Sigma do not actually charge fees. Mar 22, 2015 at 17:48
Fees are slated to begin for papers submitted on or after January 1, 2016. Jul 9, 2015 at 19:05
Journal of Mathematical Physics, which publishes articles by mathematicians, is a serious journal published by AIP that follows the AIP fee-based Open Access policy : http://publishing.aip.org/librarians/open-access-policy
The UK as a whole is moving towards using open access, so most of the UK maths journals, and a proportion of others, now offer open access in some form (although that can mean allowing you to put the final draft on a repository, called 'green open access'). The LMS has created the Transactions, which is fully open access ('gold').
1The UK as a whole is moving away from author-pay open access Jul 9, 2015 at 15:13
The recent Analysis and geometry in metric spaces, while maybe not yet well-established, is as far as I can tell (after exchange with the editorial board at some occasions) trustworthy as any math journal; this is witnessed by the impressive editorial board.
In general, journals reviewed in MathSciNet are trustworthy. So check there for the journal you are considering.
6I would say that a "fishy journal" is going to be dropped by MathSciNet sooner or later. I have, unfortunately, a paper published in a journal which I think is on the borderline between being legit and being fishy. One of the things I did was look to see that MathSciNet covered it, as you suggested. However, I did not notice that MathSciNet has stopped covering it almost a year before (this is much clearer a year or two later than it was then, but I should have looked more carefully). And when I submitted they advertised as being covered on MathSciNet! Anyway: be careful out there... Mar 22, 2015 at 17:11
Research in the Mathematical Sciences is very reputable, if new. The editor in chief is Ken Ono.
For the down-voter: when I wrote this RiMS was in fact fee-based open access, but it has since been converted to a subscription journal with the usual double-dip-risking optional pay-for-open-access. See mathoverflow.net/questions/309002/… for some details. Sep 10, 2018 at 2:08