Let be a uniformly convex Banach space and be a nonexpansive semigroup such that . Consider the iterative method that generates the sequence by the algorithm , where , , and are three sequences satisfying certain conditions, is a contraction mapping. Strong convergence of the algorithm is proved assuming either has a weakly continuous duality map or has a uniformly Gâteaux differentiable norm.
"Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 19, 2012. https://doi.org/10.1155/2012/641479