I cannot update the phone, only a message but no update available

There are two types of updates, iOS updates and carrier setting updates. Post a screenshot of the message if you can.

Update your carrier settings on your iPhone or iPad

https://support.apple.com/en-us/HT201270

csilla16 Said:

"i have no cellular function, have an update message but no update available. Have no shame Apple?"

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Use of a Computer to Update:

My User Tip: Making Use of a Computer for Updating an iOS Device - User Tip