Also, Voi and vostre are used in formal situations. It is the formal of tu or tue. You would only use tu for family, close friends and people you really know. So, if you are speaking about someone you do not know (are not familiar with) or addressing an elder, you would use voi instead.
You are right, voi is sometimes used in formal situations (to address one person) but it is not common and mostly older people use it. http://forum.wordreference.com/showthread.php?t=185531
More common formal "you" is "Lei" (notice the capital "L") which is 3. person singular so the sentence could also go like this :
- Non mangiamo le sue banane. = We do not eat your bananas.
The Italian possessive adjectives are preceded by definite articles and agree in gender and number with the noun possessed, not with the possessor. http://italian.about.com/library/fare/blfare132a.htm