Problem Tenants!

[Jason Fang]

I inherited some problem tenants from a rental property I recently purchased.  I closed at the beginning of the month, we talked about bring their rent up to market rents, and then they went on vacation.  Their current rent is about 25% under market.  When they return, they ask us to confirm that we are increasing their rent then they say that we must give them 30 day written notice of any rent increase.  Their previous lease had been terminated by the seller.  Do they have any grounds?  There is no contractual relationship between the tenants and me, correct?  I have a right to charge the market rent, is that correct?  Because they insisted, I lowered my first month's rent as a gesture of goodwill but I feel like I've been cheated just because they are being stubborn.  She comes back from vacation and then tells me she cannot afford an increase of $105?  Really?

Who is in the right here?