Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces (Q1015839)

Let \(C\) be a nonempty closed convex subset of a real Banach space \(X\) whose norm is uniformly Gâteaux differentiable and let \(T : C\to C\) be a continuous pseudocontraction with nonempty fixed point set \(F(T)\). A sequence \((x_n)\) is defined iteratively which converges strongly to a fixed point of \(T\). For all the continuous pseudocontractive mappings for which it is possible to construct the sequence \((x_n)\), the obtained result improves and extends a recent result of \textit{Y.-H. Yao}, \textit{Y.-C. Liou} and \textit{R.-D. Chen} [Nonlinear Anal., Theory Methods Appl. 67, No.~12, A, 3311--3317 (2007; Zbl 1129.47059)].