In this paper, the possibility of a superconducting state mediated by the valence fluctuations in Ce-based heavy-fermion systems under high pressure is investigated for the extended periodic Anderson model. In this extended version, an additional local Coulomb repulsion between the localized and conduction electrons is included. In the framework of the projector-based renormalization method, we derive self-consistent equations for the superconducting order parameters. Our numerical evaluation for a two-dimensional case specifies that superconductivity in the heavy-fermion systems has a d-wave character and is mediated by valence fluctuations. By use of some additional simplifications, a BCS-like equation is found; an effective pairing interaction then is delivered. The interaction depends strongly on momentum and becomes dominant in the valence transition regime.