The first took place at around 3.30pm on Sunday, May 8, when officers were called to reports of a robbery at a shop on Lansdowne Road.
The second occurred at around 10:35pm on the following day (Monday, May 9), when a taxi driver was allegedly threatened and robbed.
A police spokesperson, via Facebook, said: “A man has been arrested on suspicion of robbery in connection with both reports.
“A woman has also been arrested on suspicion of robbery in connection with the second incident.
“Both remain in our custody whilst enquiries continue.”