Multivalued F-Contractions and Related Fixed Point Theorems with an Application

Abstract

In this paper, we introduce the notions of $\alpha$-$F$-contractions, by combining the notions of $\alpha$-$\psi$-contraction and $F$-contraction. Using our new
notions we obtain some fixed point theorems for multivalued mappings. As an application we establish an existence theorem for integral equations. An example is also constructed to show an importance of our results.