A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings

作者：Zhou H Y^*; Cho Y J; Kang S M

来源：Fixed Point Theory and Applications, 2007, 2007(1): 64874.

DOI：10.1155/2007/64874

Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T(1), T(2) : K -> E be two weakly inward and asymptotically nonexpansive mappings with respect to P with sequences {K(n)},{l(n)} subset of [1,infinity), lim(n ->infinity) k(n) = 1, lim(n ->infinity) l(n) = 1, F(T(1)) boolean AND F(T(2)) = {x is an element of K : T(1)x = T(2)x = x} not equal empty set, respectively. Suppose that {x(n)} is a sequence in K generated iteratively by x(1) is an element of K, x(n+1) = alpha(n)x(n) + beta(n)(PT(1))(n) x(n) + gamma(n)(PT(2))(n) x(n), for all n >= 1, where {alpha(n)}, {beta(n)}, and {gamma(n)} are three real sequences in [epsilon, 1-epsilon] for some epsilon > 0 which satisfy condition alpha(n) + beta(n) + gamma(n) = 1. Then, we have the following. (1) If one of T(1) and T(2) is completely continuous or demicompact and Sigma(infinity)(n=1)(k(n) - 1) < infinity, Sigma(infinity)(n=1)(l(n) - 1) < infinity, then the strong convergence of {x(n)} to some q is an element of F(T(1)) boolean AND F(T(2)) is established. ( 2) If E is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Frechet differentiable, then the weak convergence of {x(n)} to some q is an element of F(T(1)) boolean AND F(T(2)) is proved.

• 出版日期2007
• 单位华北电力大学