If you were trying to launch the iTunes you just installed from the Dock and it did not open or start, try looking into the Applications Folder and double-click on the iTunes application itself.
If there are two iTunes applications, single click on one and use Get Info to see what version and date it is; and get rid of the older one after determining what one you recently installed. Then drag the old iTunes icon out of Dock; and drag from the new iTunes application into the Dock to put a current icon there.
Not sure if this will help...
The windows instructions
linked above likely won't.
There is this Mac OS X ASC discussion with a similar issue, that covers the topic:
https://discussions.apple.com/thread/5784659
•Troubleshooint iTunes installation on Mac OS X:
http://support.apple.com/kb/HT2311
Good luck & happy computing! 🙂