Have you tried to search this error in KB articles and apply suggested solutions? There are several KB articles about this issue.
Plesk doesn't ship MySQL, it only downloads it from original OS vendor repo. So it is not Plesk problem but system MySQL package, or MySQL from Atomic repository as I see
So, if you can't apply solutions from multiple KB articles about this issue and this is urgent issue - it would be better to ask assistance from Plesk Support Team -
https://support.plesk.com/hc/en-us/requests/new
Yes atomic promlem update error
2017-03-14 03:14:14 INFO: pum is called with arguments: ['--update', '--json']
Loading mirror speeds from cached hostfile
* atomic: mirror.veriteknik.net.tr
* base: mirror.venov.net.tr
* epel: mirror.veriteknik.net.tr
* extras: mirror.venov.net.tr
* updates: mirror.dgn.net.tr
2017-03-14 03:14:16 INFO: updating packages: mysql-libs mysql-devel mysql-server mysql
Running rpm_check_debug
Updating: mysql-libs-5.5.54-36.x86_64 165/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1299/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1428/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1604/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 67296/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 132832/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 198368/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 263904/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 329440/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 394976/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 460512/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 526048/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 591584/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 657120/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 722656/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 788192/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 853728/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 919264/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 984800/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1050336/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1115872/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1181408/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1246944/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1312480/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1378016/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1443552/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1509088/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1574624/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1640160/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1705696/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1771232/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1836768/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1902304/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 1967840/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2033376/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2098912/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2164448/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2229984/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2295520/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2361056/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2426592/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2492128/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2557664/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2623200/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2688736/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2754272/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2819808/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2885344/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2950880/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2992496/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 2992640/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3010779/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3013428/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3013886/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3014016/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3014156/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3032611/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3034505/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3040186/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3045848/4296864 [1/8]
Updating: mysql-libs-5.5.54-36.x86_64 3054237/4296864 [1/8]
Cleanup: mysql-devel 100/100 [5/8]
Cleanup: mysql-server 100/100 [6/8]
Cleanup: mysql 100/100 [7/8]
Cleanup: mysql-libs 100/100 [8/8]
Verify: 1/8: mysql-libs.x86_64 0:5.5.54-36 - u
Verify: 2/8: mysql-devel.x86_64 0:5.5.54-36 - u
Verify: 3/8: mysql-server.x86_64 0:5.5.54-36 - u
Verify: 4/8: mysql.x86_64 0:5.5.54-36 - u
Verify: 5/8: mysql-libs.x86_64 0:5.5.52-36.el6.art - ud
Verify: 6/8: mysql.x86_64 0:5.5.52-36.el6.art - ud
Verify: 7/8: mysql-server.x86_64 0:5.5.52-36.el6.art - ud
Verify: 8/8: mysql-devel.x86_64 0:5.5.52-36.el6.art - ud
2017-03-14 03:14:27 INFO: pum completed successfully
2017-03-14 03:14:27 INFO: pum is called with arguments: ['--check']
Loaded plugins: fastestmirror, security