Fixed point results for $r$-$(\mathbf{\eta},\xi,\psi)$-contractive mappings of type (I), (II) and (III)

In this paper, we introduce some classes of $r$-$(\eta,\xi,\psi)$-contractive mappings and prove results of fixed point in the setting of complete metric spaces. Some examples and an application to integral equations are given to illustrate the usability of the obtained results.