Hi,
Thank you for the screenshot, unfortunately it does not contain all the details. It refers to Tablepress on the first line though, so I have tested Tablepress and Ajax Search Pro installations on multiple servers, but they all were working without issues.
I am guessing this might be related to something else as well. Can you please add temporary FTP and back-end details as well? I would like to trigger the error and debug through the plugin code directly via FTP to see where the error is exactly originated. Thank you!