Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings

Watcharaporn CholamjiakSuthep SuantaiChiang Mai UniversityMahidol University2018-09-242018-09-242010-08-01Nonlinear Analysis: Hybrid Systems. Vol.4, No.3 (2010), 524-5301751570X2-s2.0-77955589557https://repository.li.mahidol.ac.th/handle/20.500.14594/29013In this paper, we prove a weak convergence theorem for the modified Mann iteration process for a uniformly Lipschitzian and asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two new kinds of monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and asymptotically quasi-nonexpansive mappings in a Hilbert space. The results of this paper improve on and extend corresponding ones announced by many authors. © 2009.Mahidol UniversityComputer ScienceEngineeringMathematicsConvergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappingsArticleSCOPUS10.1016/j.nahs.2009.12.003