When you try to update your apps on the iPhone none seem to do so. Using the iPhone 5S as the example, here are the steps to try.
- Make sure you are logged into your Apple account successfully.
- Make sure you have Restrictions turned off. Go to Settings, General and scroll down to Restrictions. If you see the option to Disable Restrictions, tap it.
- Make sure you are connected to Wifi.
- Try updating using a different WiFi connection.
- Make sure you have at least 1 Gb of free space on your iPhone.
- Try restarting the device.
- Connect your iPhone to the computer and run the updates using iTunes.
The option to update using iTunes is what worked for me. Sync your iPhone to iTunes before running the updates. Disconnect the iPhone from the computer. In iTunes, go to the App Store Home page. (If it is not there, scroll to the bottom of the screen and click the link AppStore under the heading Explore). At the top of the screen click on My iPhone Apps. Then click Updates. Once the Apps are updated. Connect your iPhone to the computer and sync. Your phone should now have the updates installed.