Source: http://bookingtohosting..com/2015/05/error-apple-application-support-is.html
"Apple Application Support is required to run iTunes. Please uninstall iTunes, then install iTunes again".
This article applies to the following Error messages.

1. Error: (When Trying To Install iTunes ) Apple Application Support Was Not Found. Apple Application Support Is Required To Run iTunes Helper.

2. Apple Application Support was not found.


Solution:

1. Download and install WinRAR or 7-Zip .
2. Right-click the iTunesSetup.exe / iTunes64Setup.exe / iTunes6464setup.exe icon and choose "Open with WinRAR / 7-zip".
3. Once the EXE is opened in WinRAR/ 7Zip, double-click AppleApplicationSupport.msi and when the installer window is open choose "Repair" or install Apple Application Support.
4. Done! You can now run iTunes normally"

Similarly if you get the error message related to Bonjour that "Bonjour is required to run iTunes.Please uninstall iTunes and install iTunes again."

Do the same steps mentioned above, just run the Bonjour,msi to repair or reinstall it instead of AppleApplicationSupport.msi


Note:- These error messages could also be the result of improper installation of iTunes which happens when your security software blocks some of the contents of iTunesSetup.exe during installation.To Avoid this situation follow the below mentioned ste

1. Download and save iTunesSetup.exe somewhere on your harddrive.
2. Disconnect from internet.
3. Disable Firewall/Security software.
4. Run install. Note that it installs Apple Application Support and a bunch of other software this time.
5. Run iTunes.
6. Enable Firewall/Security software.
7. Reconnect to the internet.


If you have difficulty downloading the iTunes installer file try; unticking the "Keep me up to date..." box, clearing your browser's cache, changing pop-up blocker settings, using an alternate browser, or using these direct links:Read More in details here http://bookingtohosting..com/2015/05/error-apple-application-support-is.html