A fixed point theorem for F-Khan-contractions on complete metric spaces and application to integral equations

In this article, we introduce a new concept of contraction called F-Khan-contractions and prove a fixed point theorem concerning this contraction which generalizes the results announced by Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste., 8 (1976), 69–72], Fisher [B. Fisher, Riv. Math. Univ. Parma., 4 (1978), 135–137], and Piri et al. [H. Piri, S. Rahrovi, P. Kumam, J. Math. Computer Sci., 17 (2017), 76–83]. An example and application for the solution of certain integral equations are given to illustrate the usability of the obtained results.