An affirmative answer to Panyanak and Suantai's open question on the viscosity approximation methods for a nonexpansive multi-valued mapping in CAT(0) spaces

Volume 10, Issue 5, pp 2719--2726 http://dx.doi.org/10.22436/jnsa.010.05.38

Publication Date: May 25, 2017 Submission Date: October 27, 2016

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Authors

Shih-Sen Chang - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Lin Wang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China. Jen-Chih Yao - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Li Yang - Department of Mathematics, South West University of Science and Technology, Mianyang, Sichuan 621010, China.

Abstract

An affirmative answer to the open question raised by Panyanak and Suantai [B. Panyanak, S. Suantai, Fixed Point Theory Appl., 2015 (2015), 14 pages] is given. Our results also generalize the results of Panyanak and Suantai [B. Panyanak, S. Suantai, Fixed Point Theory Appl., 2015 (2015), 14 pages], Wangkeeree and Preechasilp [R. Wangkeeree, P. Preechasilp, J. Inequal. Appl., 2013 (2013), 15 pages], Dhompongsa et al. [S. Dhompongsa, A. Kaewkhao, B. Panyanak, Nonlinear Anal., 75 (2012), 459–468], and many others. Some related results in R-trees are also proved.

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Keywords

• Viscosity approximation method
• fixed point
• strong convergence
• multivalued nonexpansive mapping
• CAT(0) space.

MSC

•  47H09
•  47J25

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