Unfortunately you were looking at outdated documentation. The up-to-date documentation can be found at http://dev.twitch.tv/docs.
You can query the GET https://api.twitch.tv/kraken/streams/ endpoint described at https://dev.twitch.tv/docs/v5/reference/streams/#get-live-streams. I suppose you have a predefined list of streamers you want to check whether they are live or not? You can filter for specific channels with the channels query-parameter (note that it takes channel-ids, not names):
GET https://api.twitch.tv/kraken/streams/?channel=2344325,546456,3452345,...
you should always reference channels (users, but basically everything) by their id. if you need to turn a channel name to a channel id however, you can use this:
GET https://api.twitch.tv/kraken/users?login=name1,name2,name3,...