You can choose whether or not to receive an email notification whenever someone accepts or declines an invitation from your Calendar.
When event responses for your Google calendar are set to email, you will receive an email regarding their response.
You can turn event notifications for calendar events on or off by clicking the Google Calendar App.
From My Calendars, click Options.
Click Settings and Sharing.
From Settings for my calendars, click General notifications.
You can select Email or None. If you do not wish to receive an email whenever someone accepts or declines a calendar invitation in your email in-box, change the notification from Email to None.