Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces
Songnian He, Jun Guo · Journal of Applied Mathematics · 2012
Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, an infinite family of nonexpansive mappings with the nonempty set of common fixed points , and f : C → C a contraction. We introduce an explicit iterative algorithm xn+1 = αnf(xn)+(1 − αn)Lnxn, where and wk > 0 with . Under certain appropriate conditions on {αn}, we prove that {xn} converges strongly to a common fixed point x* of , which solves the following variational inequality: , 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.