On fixed points of some multivalued mappings under certain function classes

It is well known that the Banach contraction principle implies the existence of fixed points of single-valued mappings. On the other hand, S.B. Nadler has solved the problem that guarantees the existence of fixed point for multivalued mapping. However, we have to emphasize that similar methods are not applied for nonexpansive multivalued mappings. The aim of this study is to investigate the existence of a fixed point on nonexpansive multivalued mappings with the help of function sequences and functions having shifting distance property. In addition, some hypothesis of this work were explained with an interesting example.