Browser notifications, as in when new blog posts get published, your older visitors get a notification?
There are many web based SaaS offering this solution already, you may need to check these links out:
https://goroost.com/
https://mobiopush.com/
https://pushcrew.com
They require you to add a piece of javascript across all your pages so that they can track your users, accept permissions and deliver notifications/push messages.
After installation, you can send push notifications manually or RSS feed based notifications, more information available on sites I linked to