Let $E$ be a real uniformly smooth Banach space, $T:E\rightarrow E$ be a generalized Lipschitzian and $\Phi$-strongly accretive mapping. It is shown that under suitable conditions the Ishikawa iterative process converges strongly to the unique solution of the equation $Tx=f$. A related result deals with approximation of the unique fixed point of a generalized Lipschitzian and $\Phi$-strongly pseudo-contractive mapping.