Recent trends in effective analysis The references listed at http://en.wikipedia.org/wiki/Computable_analysis have all been published 30-15 years ago. Are the approaches which these references expose still up-to-date and relevant to the current paths of research in computable analysis? (In case they are not, where can I find a good introduction to the current trends?)
 A: (At François's request, my comment in now an answer.)
Yes, it is still an active research area. It however is spread out throughout a number of camps (traditions): The Weihrauch camp, the reverse math camp, the computability theory camp, the randomness camp, the proof theory camp, and a few different constructive math camps. (Also, see many of the quantitative results in classical analysis.) Most researchers span two or more camps, and I don't mean to imply there is a feud or anything. However, there isn't necessarily an organized central list of open problems or a central agenda. You may want to check out cca-net.de as a starting point.
Edit: You may also want to check out this survey by Brattka and Avigad.  It does a good job of explaining many of the different traditions.
A: The references you mention are all monographs (Abert, Pour-El and Richards, Simpson, Weihrauch). Here are some more recent (at most 5 years old) monographs which border on computable analysis:


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*Kohlenbach, Applied Proof Theory: Proof Interpretations and their Use in Mathematics. (A lot of the applications are in analysis.) 2008. 

*Nies, Computability and randomness. 2009.

*Downey and Hirschfeldt: Algorithmic randomness and complexity. 2010.

