IPA: //əkˈnɒlɪdʒədli//
KK: /ækˈnɑːlɪdʒdli/
In a way that is openly recognized or accepted; without denial.
He acknowledgedly accepted the mistakes he made during the project.
Acknowledgedly → It is formed from "acknowledge" (from Old English *oncnawan*, meaning to recognize or admit) and the suffix "-ly" (meaning in a manner of). The word "acknowledgedly" means in a manner that recognizes or admits something.
Think of 'recognizing' something ('acknowledge') and how the '-ly' makes it a manner of doing so. So, acknowledgedly means doing something in a way that shows recognition.