I am not able to download any app from the App Store on my iPhone 5 which is running iOS 7.1.1.
I have been getting the following error since last week when attempting to download an app.
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Luckily, I could fix my issue.
I had to change my DNS to 188.8.131.52. My internet used to work before this but after changing my DNS now I am able to download apps from App Store.
But I tell I haven't changed any setting on my iPad 2 running iOS 6 still every thing works including App Store downloads. I think this issue is with iPhone 5 or definitely iOS 7.1.1.
This could also be a problem with the AppleID. A friend of mine had this problem that all of the devices registered to his account would not be able to download apps (even when another Apple ID is entered). Only help was to contact AppleCare (you can do that via the support tab on the apple website)
You can try to restart the device.
If this doesn't help, make a soft reset (you won't lose data). To make a soft reset, press the on/off button at the top and the home button until the apple icon appears (Ignore the "Slide to power off") button if it appears.
If this doesn't help, I would go to the Genius Bar