Answer
(Fatwa: 554/406=H)
If the three brothers bought big animal (e.g. buffalo), attributed one portion (out of seven) to their mother and slaughtered it then the qurbani was accepted from all four participants. If they bought a small animal (e.g. goat) and then gave the animal to one brother and he slaughtered the goat from mother then also this qurbani was valid. If two brothers gave the goat in possession of the third brother and he slaughtered the goat from himself then also the qurbani will be acceptable. If there was any other condition beside the one mentioned above then write it clearly and submit the question again.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband