Fixed point for α-Θ-φ-contractions and first-order periodic differential problem

In this paper, we use a function and two suitable families of functions, called phi and , in order to define a new type of contraction which we call --phi-contraction. We establish some fixed point results in the setting of complete metric spaces for the --phi-contractions which are -admissible mappings. Furthermore, we prove that the fixed points belong to the zero-set of a given function. Our results extend, generalize and improve many of existing theorems in the literature. In addition, we stress that, as application of our results, we give a result of existence and uniqueness for the solution of a first-order periodic differential problem. Some examples are presented to illustrate the usefulness of our finding.