Strong convergence of viscosity approximation methods with strong pseudocontraction for Lipschitz pseudocontractive mappings

摘要

In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by $$x_{n+1} = (1-alpha_n-beta_n)x_n+alpha_nf(x_n)+beta_nTx_n$$ , where f is a Lipschitz strong pseudocontractive mapping and {β n }, {α n } satisfy (i) $limlimits_{ntoinfty}alpha_n = 0$ ; (ii) $ sumlimits_{n=1}^infty alpha_n = infty$ ; (iii) $limlimits_{ntoinfty}frac{beta_n^2}{alpha_n} = 0$ .