An observation on α-type F-contractions and some ordered-theoretic fixed point results

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.