Abstract and Applied Analysis
Volume 2009 (2009), Article ID 297565, 16 pages
doi:10.1155/2009/297565

Monotone hybrid projection algorithms for an infinitely countable family of Lipschitz generalized asymptotically quasi-nonexpansive mappings

Abstract

We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).