SignalR is a great way to send real time information to a web client, essentially having server-side code push information to the client and call client-side code (i.e. javascript) in realtime.
PushSharp is a great way to send push notifications to native mobile apps. For iOS, this means using Apple's infrastructure. It also means that the message will be shown as a notification in the iPhone and not just inside the browser.
Essentially, if the iPhone request you mention is coming from a native app, try PushSharp. If it's a web app running in a browser, use SignalR.