A general degree for function triples

Consider a fixed class of maps $F$ for which there is a degree theory\nfor the coincidence problem $F(x)=\\varphi(x)$ with compact $\\varphi$.\nIt is proved that under very natural assumptions this degree extends\nto a degree for function triples which in particular provides a degree\nfor coincidence inclusions $F(x)\\in\\Phi(x)$.