How to delete your apps in the purchase section in the app store on an iphone 4?

The "not on this iphone" section

Added (1). That swipe thing that everyone says to do doesn't work!

Can you provide more detail? As your question is vague at best, but if you are saying removing purchase you made on app store and not removing it from your iphone, unfortunately, you can't do it automatically on the app store, I suggest you contact Apple Apps Store for cancelling service, as they are the only people know how to. Purchase apps are marked down as a history in your account, in the event that you need to re-download your apps, its still available. It can't be deleted or removed unless full authorization from you.

A question, you should know, deleting purchase apps does not give you any sort of refund, no compensation and no damages claim… Why would you want to delete them? Is it something wrong for your purchase apps?