A fixed point theorem for generalized \(F\)-contractions on complete metric spaces. (English) Zbl 1346.54020
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 \(y\)).
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 \(y\)).
Reviewer: Ravindra Kishor Bisht (Pune)
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
References:
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