SHRINKING PROJECTION ALGORITHM FOR FIXED POINTS OF FIRMLY NONEXPANSIVE MAPPINGS AND ITS APPLICATIONS
Jinlong Kang, Yongfu Su, Xin Zhang · 2010
The purpose of this paper is to study the shrinking projection method for finding common fixed points of firmly nonexpansive mappings. Some strong convergence theorems are proved. The main convergence theorem is also applied to the equilibrium and optimization problems. The results of this paper improve and extend the results of Koji Aoyama, Fumiaki Kohsaka, Wataru Takahashi (Koji Aoyama, Fumiaki Kohsaka, Wataru Takahashi, Shrinking projection methods for firmly nonexpansive mappings, Nonlinear Analysis (2009), 71(2009), 1626-1632) in the following respects: (1) the main convergence theorem has been proved by using the new method; (2) the condition of family of firmly nonexpansive mappings {Tn}1=1 has been relaxed from the condition (Z) to uniformly closed; (3) the application has been given to find the solution of equilibrium and