I'm looking for an RSS reader that has push notifications but I can also filter the RSS feed, like there's an RSS feed I need to subscribe to but I only want to be notified about posts that contain a certain word in the title.
The suitable named Push Reader app seems to be what I'm looking for, it has push notifications that we filtered by keywords, not exactly sure where the keywords are used to filter (like body or title etc) but as far as I can see it's pretty good.
Edit: it filters by keyword at least in the title. I just got a push notification telling me I have homework ;)
There are no RSS readers for iOS which match your feature set yet, however there might be some in the future.
you can try Pulse app for iPhone. here is the location http://itunes.apple.com/us/app/pulse-news-mini/id377594176?mt=8