In this paper, we introduce the concept of $\alpha$-$\psi$-$\xi$-contractive mappings and $\beta$-$\psi$-$\xi$-contractive multifunctions and give some fixed point results for such mappings and multifunctions. We show that our fixed point result of $\alpha$-$\psi$-$\xi$-contractive mappings is different from that of $\alpha$-$\psi$-contractive mappings which has been proved recently by Samet, Vetro and Vetro.