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

摘要

In this work, we introduce the new concept of a generalization of (F,φ)-contraction mapping and establish some existence results of φ-fixed point for such mappings. We also state some illustrative examples to support our results and give numerical experiment for approximating the φ-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.