A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings
1 Department of Applied Mathematics, North China Electric Power University, Baoding 071003, China
2 Department of Mathematics Education and RINS, College of Natural Sciences, Gyeongsang National University, Chinju 660-701, South Korea
Fixed Point Theory and Applications 2007, 2007:064874 doi:10.1155/2007/64874Published: 21 May 2007
Suppose that is a nonempty closed convex subset of a real uniformly convex and smooth Banach space with as a sunny nonexpansive retraction. Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences , , respectively. Suppose that is a sequence in generated iteratively by , , for all , where , , and are three real sequences in for some which satisfy condition . Then, we have the following. (1) If one of and is completely continuous or demicompact and , then the strong convergence of to some is established. (2) If is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Fréchet differentiable, then the weak convergence of to some is proved.