Let E be a real q -uniformly smooth Banach space which is also uniformly convex (e.g., L p or l p spaces ( 1 < p < ∞ ) ) , and K a nonempty closed convex subset of E . By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a κ -strictly pseudocontractive mapping of Browder-Petryshyn type on K in condition thet the control sequence { α n } is chosen so that (i) μ ≤ α n < 1 , n ≥ 0 ; (ii) ∑ n = 0 ∞ ( 1 − α n ) [ q κ − C q ( 1 − α n ) q − 1 ] = ∞ , where μ ∈ [ max ⁡ { 0 , 1 − ( q κ / C q ) 1 / ( q − 1 ) } , 1 ) . Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.