A multivalued fixed point result with associated data dependece and stability study

In this paper, our primary result is on the existence of non-empty fixed point sets for a new multivalued function defined here. An admissibility condition is also postulated and used in the main theorem. In two separate sections, we present data dependence and stability results for the non-empty fixed-point sets of these mappings. Some consequences of the main theorem are discussed. The analysis is in the most general setting of metric spaces. An illustrative example is discussed, which shows that our existence theorem effectively extends some results in this line of research.