Unable to update app

Why and how to update my iphone or ipad apps when out of 100 apps that are meant to be updated, only half are able to be updated. Later realised that this half belong to my existing Apple ID, the other half keep prompting me for my old Apple ID and password that no more exist.

Which means that those Purchased paid apps are no more in itunes system for future updates because itunes no more recognise the old Apple ID.

So is there a way of getting back to updating those apps?