IPhone won’t be able to Update Apps, if there is restriction placed on Installation of Apps on your device. Note: Enable Automatic Downloads under “Cellular Data” section, only if you are on Unlimited Data Plan. Make sure iPhone is set to automatically download App updates by going to Settings > App Store > on the next screen, make sure the toggle next to App Updates is set to ON position. Enable Automatic Downloads for App Updates
You should be able to fix this problem using any of the methods as listed below.