imap ? Not sure what that means.
What he's asking is basically, we need more information. What account are you using? Is it gmail, yahoo, .mac, aol...what?
If it's yahoo or gmail or another email account that has imap capability, then we need to ask if you access the same email account elsewhere, like a work computer? If so, if it's an imap account, anything you do on that computer will be mirrored on your iphone. Imap is a server side sync of the email. If you do it on the phone, it will be reflected on your computer and everywhere else you see that account.
So, simply, have you deleted those emails on another device or computer?