GENERALIZED WEAKLY α-CONTRACTIVE MAPPINGS AND APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS.

In this paper, we introduce the notion of generalized weakly α-contractive mappings and give some common fixed point results for this type of contraction. The presented theorems extend, generalize and improve many existing results in the literature. Two examples as well as an application to ordinary differential equations are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]