On contractions involving an auxiliary mapping and fixed-point results

For a given metric space (M,d), we introduce two classes of mappings F: M ? M satisfying contractions involving an auxiliary mapping S: M ? M ? M. For each class, we study the existence and uniqueness of fixed points. Iterative algorithms converging to the fixed points, as well as the size of the convergence errors, are also provided. For particular choices of the auxiliary mapping S, we recover the Banach and Kannan fixed-point theorems. Some examples illustrating the obtained results and an application to cyclic contractions are given.