A fixed point theorem for generalized \(F\)-contractions on complete metric spaces (Q895837)

In the present paper, the authors obtain a fixed point theorem for a generalized \(F\)-contraction defined on a metric space. More specifically, given a metric space \(X\) and a mapping \(T\), they give sufficient conditions for the existence of a point \(z \in X\) such that \(z = Tz\). They also give an application of their result to the existence of solutions of some class of integral equations.The results of the paper improve and extend a host of previously known results and are useful to researchers in nonlinear analysis, particularly, in the area of fixed point theory. Reviewer's remark: Due to symmetricity condition in a metric space, the authors should also verify dual of the condition of generalized \(F\)-contractions (by interchanging the roles of the points \(x\) and \(y\)).