On monotone multivalued transformations


Authors

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. - Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U.S.A.


Abstract

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.


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