WEAK AND STRONG CONVERGENCE THEOREMS FOR POSITIVELY HOMOGENEOUS NONEXPANSIVE MAPPINGS IN BANACH SPACES - Takahashi, Wataru; Yao, Jen-Chih (Taiwanese journal of mathematics, 2011)
Our purpose in this paper is first to prove a weak convergence theorem by Mann's iteration for positively homogeneous nonexpansive mappings in a Banach space. Further, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such mappings. From two results, we obtain weak and strong convergence theorems for linear contractive mappings in a Banach space. These results are new even if the mappings are linear and contractive. 2000Mathematics Subject Classification: 47H05, 47H09, 47H20. Key words and phrases: Banach space, Nonexpansive mapping, Fixed point, Generalized nonexpansive mapping, Hybrid method, Mann's iteration.