On monotone multivalued transformations


Buthinah A. Bin Dehaish - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia Mohamed A. Khamsi - Department of Mathematics \(\&\) Statistics, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia and Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U.S.A.


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.