The Execute method of job definition Microsoft.Office.Server.UserProfiles.UserProfileImportJob (ID ) threw an exception. More information is included below.An update conflict has occurred, and you must re-try this action. The object UserProfileApplication Name=User Profile Service App was updated by sharepointfarm, in the w3wp (3936) process, on machine Database server. View the tracing log for more information about the conflict.

Got the execute methdod error when stopping/startig user profile services , followed the below steps and it worked for me.

Accounts:

Domainname\sharepointsuperuser

Domainname\sharepointsuperreader       

Launch SharePoint 2010 Management console to run the powershell commands

$webportal = Get-SPWebApplication -Identity "SharePoint - 39051"

$webportal.Properties["portalsuperuseraccount"] = "domainname\sharepointsuperuser"

$webportal.Properties["portalsuperreaderaccount"] = "domainname\ sharepointsuperreader"

$webpoportal.Update()

Executed iisreset and issue  resolved for me