Is there a possibility so see from some unix log file what process have invoked a bash/ksh shell script or is this shell script invoked manually from command line? So is there some log file which stores this kind of history automatically?
Unless you have audit logging enabled there isn't typically any way to see a log of what scripts were executed postmortem.
If it was a script that was executed from a a scheduler such as
at then these will show up in various log files under
/var/log, in different log files depending on which Linux distro you're using.