In this paper, we introduce a new class of contractions which remains a mixed type of weak and F-contractions but not any of them.

We observe that all the results involving \(\alpha\)-type F-contractions are not correct in their present forms. In this article, we prove some fixed point results for extended F-weak contraction mappings in metric and ordered-metric spaces. Our observations and the usability of our results are substantiated by using suitable examples. As an application, we prove an existence and uniqueness result for the solution of a first-order ordinary differential equation satisfying periodic boundary conditions in the presence of either its lower or upper solution.

In this article, we prove some existence and uniqueness fixed point results for F-expansive mappings in partially ordered metric spaces. We support the usability of our results adopting suitable examples.