FINDING COMMON FIXED POINTS OF A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS IN A BANACH SPACE
Koji Aoyama, Yasunori Kimura, Wataru Takahashi, Masashi Toyoda · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2007
The main purpose of this paper is to study an iteration procedure for find- ing a common fixed point of a countable family of nonexpansive mappings in Banach spaces. We introduce a Mann type iteration procedure. Then we prove that such a se- quence converges weakly to a common fixed point of a countable family of nonexpansive mappings. Moreover, we apply our result to the problem of finding a common fixed point of a pair of nonexpansive mappings and the problem of finding a common solution of the fixed point problem and the variational inequality problem.