We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.
Lu-Chuan Ceng. Ching-Feng Wen. Chin-Tzong Pang. "Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces." Abstr. Appl. Anal. 2014 (SI57) 1 - 15, 2014. https://doi.org/10.1155/2014/173461