# On monotone multivalued transformations

Volume 10, Issue 10, pp 5321--5327
Publication Date: October 20, 2017 Submission Date: April 17, 2017
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### 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.

### Share and Cite

##### ISRP Style

Buthinah A. Bin Dehaish, Mohamed A. Khamsi, On monotone multivalued transformations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5321--5327

##### AMA Style

Bin Dehaish Buthinah A., Khamsi Mohamed A., On monotone multivalued transformations. J. Nonlinear Sci. Appl. (2017); 10(10):5321--5327

##### Chicago/Turabian Style

Bin Dehaish, Buthinah A., Khamsi, Mohamed A.. "On monotone multivalued transformations." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5321--5327

### Keywords

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

•  47H10
•  46B99

### References

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