Fixed point theorems for asymptotic mappings of a generalized contractive type in complete metric spaces

We consider an asymptotic version of $\alpha$-$\psi$ contractive mappings. We show the existence and uniqueness of fixed points. Caccioppoli's fixed point theorem is deduced from main results in this paper. Moreover, we discuss an asymptotic version of mappings related with $(c)$-comaprison functions.