By this question you are assuming that the sex of a character is all-determining in her role. I am not convinced that this is a good starting point around which you can build a thesis. Say, for example, if you asked the question "What is the function of the man in Shakespeare's writings?" There I'm pretty sure you would agree that the characters and their roles are too divergent to draw a common line. The same can be said of Shakespeare's female characters, too.
If you want to write a theme paper along the lines of a gender study, read at least three works and then see if there is a common vein or complete contrast of the female characters therein. Limit your study to a few works rather than trying to formulate a global statement where everything "fits" - as in real life experience, it just doesn't!
Below are some references which might get you off to a good start.