A New Type of F-Contraction and Their Best Proximity Point Results with Homotopy Application

In the present paper, we aim to extend and unify the results obtained for the multivalued F-contractions, which have been frequently studied recently, in a different way from the results in the literature without using the Pompeiu-Hausdorff metric. Hence, we first introduce a new class of multivalued mappings that includes multivalued F-contractions. Then, we obtain some best proximity point results for new kind of F-contraction mappings. Thus, we unify and improve many results in the literature. To see this fact, we give some nontrivial and interesting examples. Also, considering the strong relationship between homotopy theory and various branches of mathematics, we obtain an application to homotopy theory of our main result.