Strong convergence theorems by hybrid methods for families of relatively nonexpansive mappings in Hilbert spaces

Abstract

In 2008, Takahashi, Takeuchi and Kubota [10] proved a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalized Nakajo and Takahashi's theorems [6]. Furthermore, they obtained another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. In this paper, we extend Takahashi, Takeuchi and Kubota's results for a single relatively nonexpansive mapping or a family of relatively nonexpansive mappings in a Hilbert space. Using these results, we obtain some new strong convergence theorems in a Hilbert space. © 2010 yokohama publishers.