Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces

Let be a uniformly convex Banach space and ={()∶0≤<∞} be a nonexpansive semigroup such that ⋂()=>0(())≠∅. Consider the iterative method that generates the sequence {} by the algorithm +1=()++(1−−)(1/)∫0(),≥0, 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