Existence of fixed points of generalized set-valued $F$-contractions of $b$-metric spaces

This paper deals with the existence of non-empty fixed point sets of newly introduced generalized set-valued $F$-contractions of $b$-metric spaces. Some illustrative examples show that the new results in this paper generalize properly, unify and extend some related results in the existing literature. Moreover, we extract some important consequences of the results in $b$-metric spaces. Particularly, by setting $b$-metric constant equal to one, we obtain some specific cases showing notable enhancement of existing results yet in metric spaces.