What is the ruling on inviting female students at the university who draw attention due to their clothing and mannerisms, and is it permissible for them to speak with girls in mixed-gender areas of the library for the purpose of da'wah?

Calling people to Allah is one of the best and most obligatory deeds for every Muslim man and woman. It is a cause for guidance and great reward. There is no harm for female students in inviting girls in the library and speaking with them, provided they adhere to Islamic guidelines, such as wearing the proper hijab and avoiding unlawful mixing. Young men must lower their gaze.