A new contractive condition approach to φφ-fixed point results in metric spaces and its applications

In this work, we introduce the new concept of a generalization of (F,φ)(F,φ)-contraction mapping and establish some existence results of φφ-fixed point for such mappings. We also state some illustrative examples to support our results and give numerical experiment for approximating the φφ-fixed point in this example. As an application, the obtained results are used to deduce some fixed point theorems in partial metric spaces and the application to nonlinear integral equations is given in order to illustrate the effectiveness of the main results.