My new downloaded apps won't open they are in the purchases section of my App Store but won't open?

Try:

• Reset the iOS device (no data will be lost). Press and hold the Home and sleep/wake buttons until the Apple logo appears. See if the problem persists after the device reboots (it might take a while).
• Download any free app, and then see if any of the other apps, after being re-downloaded, will open.

Good luck!

I know this sounds weird, but try downloading another app. Any free app is fine. Then try to open one of your purchased apps.