Is the iTunes app still in your Application folder?
A lot of people reported problems launching iTunes after the Yosemite 10.10.3 update.
Try this.
Go to your Applications folder, select iTunes, go to Finder > File > Get info and in the window that appears, go to Sharing & Permissions, unlock the padlock with your password, and change all permissions to Read & Write. You can now drag the iTunes app to the trash. Go to iTunes tab at the top of this page and download and install iTunes.
See this thread. Yosemite slow opening and cannot open itunes