On monotone multivalued transformations

In this work, we discuss the recently introduced monotone \(\tau\)Opial condition in Banach spaces which admit a sequence of monotone approximations of the identity. Then we give a fixed point theorem for monotone multivalued nonexpansive mappings in Banach spaces satisfying the monotone \(\tau\)Opial condition. This result generalizes those of Markin, Browder and Lami Dozo to monotone mappings.