What I must to do to verify if the user has the last version of my app on Google Play. If the user doesn't have the last one I will put him to download it.
You can use in-app-updates to give updates to your app(but this supports API 21 and above)
Supporting API level 21 and above, the Play Core library now allows us to offer in-app updates to our users — meaning we can show that an app update is available whilst the user is within the context of our application
If you want to force the user to update the app, you can use an Immediate type update
A full screen user experience that requires the user to update and restart the app in order to continue using the app. This UX is best for cases where an update is critical for continued use of the app. After a user accepts an immediate update, Google Play handles the update installation and app restart.
If your app satisfies the API level(ie minimum SDK is 21) follow this guideline to use in-app-updates