Iterative Methods For Approximating Fixed Points Of Nonexpansive Mappings And Application

In this paper,firstly in Hilbert spaces H,we consider the explicit averaging iterations of nonexpansive nonself mappings,and get strong convergent results. The results presented extend and improve the corresponding ones of Y.S. Song and R.D.Chen[Viscosity approximation methods for nonexpansive nonselfmappings, J.Math.Anal.Appl.321(2006)316-326]and S.Matsushita,D.Kuroiwa [Strong convergence of averaging iterations of nonexpansive mappings,J.Math. Anal.Appl.294(2004)206-214].Then,we consider another iteration,that is,the iteration of asymptotically nonexpansive mappings of the nonempty closed convex subset C to Hilbert spaces H.We use CQ methods to construct the iterations {x_n},{y_n},and get strong convergent results.The results presented extend and improve the corresponding ones of T.H.Kim,H.-K.Xu[,Strong convergence of modified Mann iterations for asympototically nonexpansive mappings and semigroups,Nonlinear Anal. 64(2006)1140-1152].Next,in q- uniformly Banach spaces,we construct iteration algorithm through sunny nonexpansive mappings to approach the solutions of a system of two nonlinear variational inequalities problem.The results presented extend and improve the corresponding ones of R.U.Verma[General convergnece analysis for two-step projection methods and applications to variational problems, Appl.Math.Lett.18(2005)1286-1292].At last,we preliminarily attempt to use computer and compare the speed of the common iterative sequences such as Picard iterative sequence,Mann iterative sequence and Ishikawa iterative sequence.The result has certain theory significance and the practical significance.