Does There exist a particular PSPACE Complete Problem which has a FPTAS algorithm?
It is possible to define artificial PSPACE-HARD problems with an FPTAS: define $f(x)=2^{|x|}+g(x)$
where $g(x)$ is a Boolean PSPACE-hard problem whose complexity is at most $2^n$, then $f$ is also PSPACE-hard, but it has an FPTAS: if $\epsilon \gt 2^{-|x|}$ then return $2^{|x|}$ else we have enough time to compute $f$ exactly.