Research Article
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:10.1155/2007/64874
Published: 21 May 2007Abstract
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.
