JVEsoft has a component suite with push notification support for Delphi XE8 Firemonkey. Push notifications allow you to communicate with a mobile app even if the user is not currently using the app. The push notification is sent to the device through either Google or Apple. The user receives the notification through the notification center in the device. Depending on how you configure the notification the user can select the notification and it launch your app. For example, if you want to notify a user that an even has occurred on the server you would send them a push notification prompting them to open your app and find out more about the event that happened. There is push notification component to handle receiving push notifications on Android, IOS, and OSX. And then there is a second component which integrates with the PushWoosh service for sending the push notifications. In addition to the push notification functionality there is also a TJVESocial component in this component suite which streamlines sharing content through Facebook, Twitter, and SinaWeibo. This is a commercial component suite and there is no free trial available. However, check out our other posts the analytics and payment components which are also included in this suite. These components should also work with Appmethod. There are also other ways to send push notifications as outlined here and here.
Head over and check out the full feature set of the JVEsoft component suite with push notifications and social sharing for Delphi XE8 Firemonkey.