There is no exact equivalent. Please read this: https://developer.apple.com/library/ios/documentation/iPhone/Conceptual/iPhoneOSProgrammingGuide/BackgroundExecution/BackgroundExecution.html
The relevant part:
For tasks that require more execution time to implement, you must request specific permissions to run them in the background without their being suspended. In iOS, only specific app types are allowed to run in the background:
- Apps that play audible content to the user while in the background, such as a music player app
- Apps that record audio content while in the background
- Apps that keep users informed of their location at all times, such as a navigation app
- Apps that support Voice over Internet Protocol (VoIP)
- Apps that need to download and process new content regularly
- Apps that receive regular updates from external accessories
Apps that implement these services must declare the services they support and use system frameworks to implement the relevant aspects of those services. Declaring the services lets the system know which services you use, but in some cases it is the system frameworks that actually prevent your application from being suspended.
If the function you are trying to call does one of the above, the documentation explains how to use background tasks or other methods to accomplish that.