Let $E$ be a real Banach space with a uniformly convex dual $E^*$, let the modulus of convexity of $E^*$ satisfy $\delta_{E^*}(\epsilon) \ge C\epsilon^q$ for some $q \ge 2$ and $C > 0$, and let $K$ be a nonempty closed convex and bounded subset of $E$. Let $T: K \to K$ be a continuous strongly pseudocontractive mapping. Let $\{\alpha_n\}$ and $\{\beta_n\}$ be real sequences with $0 \le \alpha_n \le \beta_n < 1, \sum_n\alpha_n\beta^{p-1}_n < \infty$, and $1/p+ 1/q = 1$. Then the sequence $\{x_n\}$ generated by $x_1 \in K, x_{n+1} = (1-\alpha_n)x_n + \alpha_nTy_n, y_n = (1-\beta_n)x_n+ \beta_nTx_n, n \ge 1$, converges strongly to the unique fixed point of $T$. Furtheremore, error estimates of Mann iteration scheme are given.