# On monotone multivalued transformations

Volume 10, Issue 10, pp 5321--5327

Publication Date: 2017-10-20

http://dx.doi.org/10.22436/jnsa.010.10.18

### 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 and 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.

### Keywords

Fixed point, systems of projections, monotone Opial condition, monotone nonexpansive mappings, multivalued mappings