An affirmative answer to the open questions on the viscosity approximation methods for nonexpansive mappings in CAT(0) spaces

作者：Chang, Shin-Sen^*; Wang, Lin; Wang, Gang; Qin, Lijuan

来源：Journal of Nonlinear Sciences and Applications, 2016, 9(6): 4563-4570.

DOI：10.22436/jnsa.009.06.94

• Viscosity approximation method
• fixed point
• strong convergence
• multivalued nonexpansive mapping
• the nice projection property N
• CAT(0) space

We prove a strong convergence theorem of a two-step viscosity iteration method for nonexpansive mappings in CAT(0) spaces without the nice projection property N and the restriction of the contraction constant k is an element of [0, 1/2). Our result gives an affirmative answer to the open questions raised by Piatek [B. Piatek, Numer. Funct. Anal. Optim., 34 (2013), 1245-1264], and Kaewkhao et al.

• 出版日期2016
• 单位中国医科大学; 云南财经大学; 昆明学院