Approximation of fixed points of nonexpansive mappings and solutions of variational inequalities

作者：Chidume C E; Chidume C O; Ali Bashir

来源：Journal of Inequalities and Applications, 2008, 284345.

DOI：10.1155/2008/284345

Let E be a real q-uniformly smooth Banach space with constant d(q), q >= 2. Let T : E -> E and G : E -> E be a nonexpansive map and an eta-strongly accretive map which is also kappa-Lipschitzian, respectively. Let {lambda(n)} be a real sequence in [0, 1] that satisfies the following condition: C1: lim lambda(n) = 0 and Sigma lambda(n) = infinity. For delta is an element of (0, (q eta/d(q)k(q))(1/(q-1))) and sigma is an element of (0, 1), define a sequence {x(n)} iteratively in E by x0 is an element of E, x(n+1) = T lambda n +1 x(n) = (1 - sigma)x(n) + sigma[Tx(n) - delta lambda(n+1)G(Tx(n))], n >= 0. Then, {x(n)} converges strongly to the unique solution x* of the variational inequality problem VI (G, K) (search for x* is an element of K such that < Gx*, j(q) (y - x*)> >= 0 for all y is an element of K), where K := Fix(T) = {x is an element of E : Tx = x} not equal circle divide. A convergence theorem related to finite family of nonexpansive maps is also proved.

• 出版日期2008