Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces

作者：He Songnian^*; Guo Jun

来源：Journal of Applied Mathematics, 2012, 787419.

DOI：10.1155/2012/787419

Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {T-k}(k=1)(infinity) : C -> C an infinite family of nonexpansive mappings with the nonempty set of common fixed points boolean AND(infinity)(k=1) Fix(T-k), and f : C -> C a contraction. We introduce an explicit iterative algorithm x(n+1) = alpha(n)f(x(n)) + (1 - alpha(n))L(n)x(n), where L-n = Sigma(n)(k=1)(omega(k)/s(n))T-k, S-n = Sigma(n)(k=1)omega(k), and omega(k) > 0 with Sigma(infinity)(k=1)omega(k) = 1. Under certain appropriate conditions on {alpha(n)}, we prove that {x(n)} converges strongly to a common fixed point x* of {T-k}(k=1)(infinity), which solves the following variational inequality: < x* - f(x*), J(x* - p)> <= 0, p is an element of boolean AND(infinity)(k=1) Fix(T-k), where J is the (normalized) duality mapping of X. This algorithm is brief and needs less computational work, since it does not involve W-mapping.

• 出版日期2012
• 单位中国民航大学