An Implicit Iteration for a Countable Family of Nonexpansive Mappings in Banach Spaces
Weerayuth Nilsrakoo, Satit Saejung · Numerical Functional Analysis and Optimization · 2009
We introduce an implicit sequence for an infinite family of nonexpansive mappings in a uniformly convex Banach space. We prove weak and strong convergence theorems for finding a common fixed point of the mappings. Our results not only include Plubtieng et al. (Numer. Funct. Anal. Optim. 2007; 28:737–749), Kikkawa and Takahashi (Ann. Univ. Mariae Curie-Skłodowska Sect. A 2004; 58:69–78), Kimura and Takahashi (Set-Valued Anal. 2008; 16:597–619) as special cases but also are established under the weaker assumptions.