iOS doesn't update apps automatically. The App Store shows notifications when the apps you've installed are updated and you need to install updates manually. Google's Play Store for Android has an option for updating apps automatically, but it's not enabled by default.
The beta version of Chrome for Android started to display an infobar that informs you there's a new version you can install: "Chrome just got better! A new version is available. Update". Sterling, a reader of this blog, noticed the notification when visiting the Chrome Releases blog, but that could be a mere coincidence.
Maybe it would be more useful to ask users to enable automatic updates.
{ Thanks, Sterling. }