Iterative approximation of fixed points of Lipschitz pseudocontractive maps

Let $E$ be a $q$-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., $\ell_p, 1<p<\infty$). Let $T$ be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset $K$ of $E$ and let $\omega\in K$ be arbitrary. Then the iteration sequence $\{z_n\}$ defined by $z_0\in K, z_{n+1}=(1-\mu_{n+ 1})\omega + \mu_{n+1}y_n; y_n = (1-\alpha_n)z_n+\alpha_nTz_n$, converges strongly to a fixed point of $T$, provided that $\{\mu_n\}$ and $\{\alpha_n\}$ have certain properties. If $E$ is a Hilbert space, then $\{z_n\}$ converges strongly to the unique fixed point of $T$ closest to $\omega$.