Q: Has anyone had problems with iTunes on there iPhone not opening?

I haven't, but I'm sure with the millions and millions of users out there, SOMEONE probably has.  How does knowing this help you?

What have you done to troubleshoot YOUR issue?

I did. Mine would attempt to open but there would be nothing on the screen. If that is your problem you need to change your cookie setting to "third party..." in the settings menu for safari. Goto settings, safari, cookies and make the change. This worked for me.

I TRY MANY TIMES BUT THIS IPHONE 5S IS NOT OPEN,THIS PHONE UNDER WARRANTY AND ISTANBUL APPLE STORE DID NOT HELP ME