Convergence theorems of iterative algorithms for continuous pseudocontractive mappings (Q880314)

In the setting of a reflexive and strictly convex Banach sapce with a uniformly Gâteaux differentiable norm, the autors discuss the convergence of the viscosity iteration process to a solution of the following variational inequality problem: find \(x^*\in F(T)\) such that \[ \langle (f(x^*)-x^*,j(x-x^*)\rangle\leq 0\quad\forall x\in F(T), \] where \(j\) is the normlized dual mapping, \(f\) is a Lipschitz strongly pseudoconstractive mapping, and \(F(T)\) is the fixed point set of a continuous pseudocontractive mapping. The authors also discuss the convergence of a modified implicit iteration to solve the above problem.