Viscosity approximation methods for hierarchical optimization problems of multivalued nonexpansive mappings in CAT(0) spaces

Volume 9, Issue 10, pp 5521--5535 http://dx.doi.org/10.22436/jnsa.009.10.03

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Authors

Jinhua Zhu - College of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. Shih-Sen Chang - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Min Liu - College of Mathematics, Yibin University, Yibin, Sichuan, 644007, China.

Abstract

The purpose of this paper is to prove some strong convergence theorems for hierarchical optimization problems of multivalued nonexpansive mappings in CAT(0) spaces by using the viscosity approximation method. Our results generalize the results of [X.-D. Liu, S.-S. Chang, J. Inequal. Appl., 2013 (2013), 14 pages], [R. Wangkeeree, P. Preechasilp, J. Inequal. Appl., 2013 (2013), 15 pages], and many others. Some related results in R-trees are also given.

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Keywords

• Viscosity approximation method
• fixed point
• variational inequality
• hierarchical optimization problems
• multivalued nonexpansive mapping
• CAT(0) space.

MSC

•  47J25
•  47H09
•  47H05

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